Как передавать логин из базы данных в другие окна?

Код, который вы предоставляете, должен быть воспроизводимый.

НИКОГДА НЕ ИЗМЕНЯЙТЕ код, сгенерированный Qt Designer, НИКОГДА.
Создайте другой класс, который наследуется от соответствующего виджета, и используйте созданный класс для его заполнения.

Я сделал некоторые заметки в своем примере.

Я увидел вашу задачу так:

main.py:

import random
import sqlite3
from PyQt5 import QtCore, QtGui, QtWidgets
from PyQt5.QtCore import pyqtSignal, QThread
from PyQt5.QtWidgets import QMessageBox

# ? from PyQt5.QtSql import QSqlDatabase, QSqlQuery, QSqlTableModel, QSqlQueryModel
# ? from autoswap import *
# ? import database as db
# ? from database import *


class Ui_Form(object):
    def setupUi(self, Form):
        Form.setObjectName("Form")
        Form.resize(593, 422)
        Form.setStyleSheet("background-color: rgb(0, 0, 0);")
        self.groupBox = QtWidgets.QGroupBox(Form)
        self.groupBox.setGeometry(QtCore.QRect(130, 40, 321, 321))
        self.groupBox.setStyleSheet("background-color: rgb(42, 43, 56);")
        self.groupBox.setTitle("")
        self.groupBox.setAlignment(QtCore.Qt.AlignCenter)
        self.groupBox.setCheckable(False)
        self.groupBox.setObjectName("groupBox")
        self.label = QtWidgets.QLabel(self.groupBox)
        self.label.setGeometry(QtCore.QRect(80, 10, 151, 61))
        self.label.setStyleSheet("font: 22pt \"MS Shell Dlg 2\";\n"
"border-color: rgb(31, 32, 41);\n"
"color: rgb(255, 255, 255);")
        self.label.setScaledContents(False)
        self.label.setAlignment(QtCore.Qt.AlignCenter)
        self.label.setObjectName("label")
        self.lineEdit = QtWidgets.QLineEdit(self.groupBox)
        self.lineEdit.setGeometry(QtCore.QRect(70, 120, 191, 31))
        self.lineEdit.setStyleSheet("background-color: rgb(31, 32, 41);\n"
"border-color: rgb(31, 32, 41);\n"
"color: rgb(211, 211, 211);")
        self.lineEdit.setText("")
        self.lineEdit.setAlignment(QtCore.Qt.AlignCenter)
        self.lineEdit.setObjectName("lineEdit")
        self.lineEdit_2 = QtWidgets.QLineEdit(self.groupBox)
        self.lineEdit_2.setGeometry(QtCore.QRect(70, 170, 191, 31))
        self.lineEdit_2.setStyleSheet("background-color: rgb(31, 32, 41);\n"
"color: rgb(211, 211, 211);")
        self.lineEdit_2.setText("")
        self.lineEdit_2.setAlignment(QtCore.Qt.AlignCenter)
        self.lineEdit_2.setObjectName("lineEdit_2")
        self.pushButton = QtWidgets.QPushButton(self.groupBox)
        self.pushButton.setGeometry(QtCore.QRect(20, 240, 91, 41))
        self.pushButton.setStyleSheet("background-color: rgb(255, 235, 167);\n"
"font: 14pt \"MS Shell Dlg 2\";\n"
"color: rgb(94, 102, 129);")
        self.pushButton.setObjectName("pushButton")
        self.pushButton_2 = QtWidgets.QPushButton(self.groupBox)
        self.pushButton_2.setGeometry(QtCore.QRect(130, 240, 170, 41))
        self.pushButton_2.setStyleSheet("background-color: rgb(255, 235, 167);\n"
"font: 13pt \"MS Shell Dlg 2\";\n"
"color: rgb(94, 102, 129);")
        self.pushButton_2.setObjectName("pushButton_2")
        self.label_2 = QtWidgets.QLabel(self.groupBox)
        self.label_2.setGeometry(QtCore.QRect(20, 120, 47, 21))
        self.label_2.setStyleSheet("font: 14pt \"MS Shell Dlg 2\";\n"
"color: rgb(94, 102, 129);")
        self.label_2.setAlignment(QtCore.Qt.AlignCenter)
        self.label_2.setObjectName("label_2")
        self.label_3 = QtWidgets.QLabel(self.groupBox)
        self.label_3.setGeometry(QtCore.QRect(10, 170, 61, 21))
        self.label_3.setStyleSheet("font: 10pt \"MS Shell Dlg 2\";\n"
"color: rgb(94, 102, 129);")
        self.label_3.setAlignment(QtCore.Qt.AlignCenter)
        self.label_3.setObjectName("label_3")

        self.retranslateUi(Form)
        QtCore.QMetaObject.connectSlotsByName(Form)

    def retranslateUi(self, Form):
        _translate = QtCore.QCoreApplication.translate
        Form.setWindowTitle(_translate("Form", "Form"))
        self.label.setText(_translate("Form", "Log IN!"))
        self.pushButton.setText(_translate("Form",  "Войти"))               # Sign In
        self.pushButton_2.setText(_translate("Form", "Зарегистрироваться")) # Sign Up
        self.label_2.setText(_translate("Form", "Login"))
        self.label_3.setText(_translate("Form", "Password"))


class Ui_MainWindow(object):
# ?    db_start()                                                          # ?
# ?    login = pyqtSignal(str, str)                                        # ?
# ?    print(login)                                                        # ?
    def setupUi(self, MainWindow):
        MainWindow.setObjectName("MainWindow")
        MainWindow.resize(800, 600)
        MainWindow.setStyleSheet("background-color: rgb(0, 0, 0);")
        self.centralwidget = QtWidgets.QWidget(MainWindow)
        self.centralwidget.setObjectName("centralwidget")
        self.groupBox = QtWidgets.QGroupBox(self.centralwidget)
        self.groupBox.setGeometry(QtCore.QRect(0, -40, 211, 631))
        self.groupBox.setStyleSheet("background-color: rgb(255, 255, 255);")
        self.groupBox.setTitle("")
        self.groupBox.setObjectName("groupBox")
        
        self.pushButton = QtWidgets.QPushButton(self.groupBox)
        self.pushButton.setGeometry(QtCore.QRect(0, 40, 211, 71))
        self.pushButton.setStyleSheet("color: rgb(255, 255, 255);\n"
"font: 18pt \"MS Shell Dlg 2\";\n"
"\n"
"background-color: rgb(85, 85, 255);\n"
"image: url(:/newPrefix/199-1999586_png-file-house-icon-png.png);")
        self.pushButton.setObjectName("pushButton")
        
        self.pushButton_5 = QtWidgets.QPushButton(self.groupBox)
        self.pushButton_5.setGeometry(QtCore.QRect(0, 530, 211, 71))
        self.pushButton_5.setStyleSheet("color: rgb(255, 255, 255);\n"
"font: 17pt \"MS Shell Dlg 2\";\n"
"\n"
"background-color: rgb(85, 85, 255);\n"
"image: url(:/newPrefix/199-1999586_png-file-house-icon-png.png);")
        self.pushButton_5.setObjectName("pushButton_5")
        
        self.pushButton_2 = QtWidgets.QPushButton(self.centralwidget)
        self.pushButton_2.setGeometry(QtCore.QRect(340, 10, 351, 131))
        self.pushButton_2.setStyleSheet("background-color: rgb(255, 255, 255);\n"
"color: rgb(0, 0, 0);\n"
"font: 16pt \"MS Shell Dlg 2\";")
        self.pushButton_2.setObjectName("pushButton_2")
        
        self.pushButton_3 = QtWidgets.QPushButton(self.centralwidget)
        self.pushButton_3.setGeometry(QtCore.QRect(340, 160, 351, 131))
        self.pushButton_3.setStyleSheet("background-color: rgb(255, 255, 255);\n"
"color: rgb(0, 0, 0);\n"
"font: 16pt \"MS Shell Dlg 2\";")
        self.pushButton_3.setObjectName("pushButton_3")
        
        self.pushButton_4 = QtWidgets.QPushButton(self.centralwidget)
        self.pushButton_4.setGeometry(QtCore.QRect(340, 310, 351, 131))
        self.pushButton_4.setStyleSheet("background-color: rgb(255, 255, 255);\n"
"color: rgb(0, 0, 0);\n"
"font: 16pt \"MS Shell Dlg 2\";")
        self.pushButton_4.setObjectName("pushButton_4")
        
        MainWindow.setCentralWidget(self.centralwidget)
        self.menubar = QtWidgets.QMenuBar(MainWindow)
        self.menubar.setGeometry(QtCore.QRect(0, 0, 800, 21))
        self.menubar.setObjectName("menubar")
        MainWindow.setMenuBar(self.menubar)
        self.statusbar = QtWidgets.QStatusBar(MainWindow)
        self.statusbar.setObjectName("statusbar")
        MainWindow.setStatusBar(self.statusbar)

        self.retranslateUi(MainWindow)
        QtCore.QMetaObject.connectSlotsByName(MainWindow)

    def retranslateUi(self, MainWindow):
        _translate = QtCore.QCoreApplication.translate
        MainWindow.setWindowTitle(_translate("MainWindow", "MainWindow"))
        self.pushButton.setToolTip(_translate("MainWindow", "<html><head/><body><p><img src=\"Ok.png\"/></p></body></html>"))
        self.pushButton.setText(_translate("MainWindow", "Home"))
        self.pushButton_5.setToolTip(_translate("MainWindow", "<html><head/><body><p><img src=\":/newPrefix/199-1999586_png-file-house-icon-png.png\"/></p></body></html>"))
        self.pushButton_5.setText(_translate("MainWindow", "Регистрация/вход"))
        self.pushButton_2.setText(_translate("MainWindow", "Автосвап"))
        self.pushButton_3.setText(_translate("MainWindow", "Выкл автосвап"))
        self.pushButton_4.setText(_translate("MainWindow", f"Настройки автосвапа"))

                
# !!! +++ vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
class Ui_Settings_autoswap(object):
    def setupUi(self, MainWindow):
        MainWindow.setObjectName("MainWindow")
        MainWindow.resize(400, 600)
        MainWindow.setStyleSheet("background-color: rgb(77, 77, 0);")
        self.centralwidget = QtWidgets.QWidget(MainWindow)
        self.centralwidget.setObjectName("centralwidget")
        self.label = QtWidgets.QLabel(self.centralwidget)
        self.label.setStyleSheet("background-color: #3aa; font-size: 25px; color: #fff;")
        self.label.setText("Тут Настройки автосвапа")
        self.label.setAlignment(QtCore.Qt.AlignCenter)
        
        self.layout = QtWidgets.QVBoxLayout(self.centralwidget)
        self.layout.addWidget(self.label)
        self.setCentralWidget(self.centralwidget)
# +++ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^


# --->vvvvvvvv           vvvvvvv  vvvvvvv <----------------------------------------
class SignInUp(QtWidgets.QWidget, Ui_Form):
    def __init__(self, parent=None):                                # !!! + parent
        super(SignInUp, self).__init__(parent)                      # !!! + parent
        self.setupUi(self)  

        self.pushButton_2.clicked.connect(self.reg)
        self.pushButton.clicked.connect(self.login_sign_in)
        
        self.lineEdit.setFocus()
        
        self.login = None                                           # !!! +++
        self.cur = parent.cur                                       # !!! +++
        self.conn = parent.conn                                     # !!! +++
        self.parent = parent                                        # !!! +++ 

    def reg(self):
        if (not self.lineEdit.text().strip()) or (not self.lineEdit_2.text().strip()):
            msg = QtWidgets.QMessageBox.information(None,
                'Внимание',
                'Заполните поля входа.')
            return
######            
        login = self.lineEdit.text()  
        password = self.cur.execute(
            'SELECT password FROM users WHERE username = ?',
                (login,)).fetchone()
                
        #print(f'{password} ------ {not password is None}') 
        if not password is None:
            msq = QMessageBox()
            msq.setWindowTitle("Регистрация")
            msq.setText(f"Пользователь с именем {login} уже зарегистрирован в БД, \n"
                        "повторите попытку регистрации еще раз."
            )
            x = msq.exec_()            
            return    

        login = self.lineEdit.text()
        password = self.lineEdit_2.text()
        self.cur.execute('INSERT INTO users (username, password) VALUES (?, ?)',
                    (login, password))
        self.conn.commit()
        
        msq = QMessageBox()
        msq.setWindowTitle("Регистрация")
        msq.setText("Вы успешно зарегистрировались!")
        x = msq.exec_()

        coord_X, coord_y, button = [random.randint(1, 1000)  for _ in range(3)]
        self.cur.execute('INSERT INTO settings_autoswap (login, coord_X, coord_y, button) VALUES (?, ?, ?, ?)',
                    (login, coord_X, coord_y, button))
        self.conn.commit()
# ??? ?        
        ''' ?????????????????????????????????
        self.home = QtWidgets.QMainWindow()
        self.ui = Ui_MainWindow()
        self.ui.setupUi(self.home)
        self.home.show()
        '''
        
    # Sign In Войти
    def login_sign_in(self):
        if (not self.lineEdit.text().strip()) or (not self.lineEdit_2.text()):
            msg = QtWidgets.QMessageBox.information(None,
                'Внимание',
                'Заполните поля входа.')
            return
    
        self.login = self.lineEdit.text()  
        password = self.cur.execute(
            'SELECT password FROM users WHERE username = ?',
                (self.login,)).fetchone()

        if (password is None) or (password[0] != self.lineEdit_2.text()):
            msq = QMessageBox()
            msq.setWindowTitle("Вход")
            msq.setText("Неверный Логин или пароль, \nповторите попытку! "
                        "или выполните регистрацию."
            )
            msq.exec_()
            self.login = None
            self.parent.pushButton_2.setEnabled(False)
            self.parent.pushButton_3.setEnabled(False)
            self.parent.pushButton_4.setEnabled(False)
        else:
            msq = QMessageBox()
            msq.setWindowTitle("Вход")
            msq.setText("Вы успешно Вошли!")
            msq.exec_()
            
            self.parent.successfully_logged()                          # !!! parent
            self.close()
        
# --->vvvvvvvvvvvvvvvv           vvvvvvvvvvv  vvvvvvvvvvvvvvvvvvvv <---------------
class SettingsAutoswap(QtWidgets.QMainWindow, Ui_Settings_autoswap):
    def __init__(self, parent=None):                                    # !!! parent
        super(SettingsAutoswap, self).__init__(parent)                  # !!! parent
        self.setupUi(self)
        #     vvvvvv                                                    !!! parent
        s_a = parent.cur.execute(
            'SELECT * FROM settings_autoswap WHERE login = ?',
                (parent.login,)).fetchone()
        # print(s_a)
        self.label.setText(f'{self.label.text()}\n\n{parent.login}\n\n{s_a}')


# +++ vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
class Thread(QThread):
    value_changed = pyqtSignal(str)

    def __init__(self, login):
        super().__init__()
        self.login = login    
        self.running = True
        
    def run(self, *args, **kwargs):
        while self.running:
            # !!! тут ваши действия, которые занимают некоторое время
            '''
            x = 459
            y = 1402
            Color = pyautogui.screenshot().getpixel((x, y))
            print(Color)
            if Color == (185, 185, 185):
                pyautogui.press("2", presses=4, interval=0.01)
            '''

            c = """background-color: {};""".format(
                QtGui.QColor(*random.sample(range(255), 3)).name()
            )

            self.value_changed.emit(c) # Излючаем сигнал и передаем аргументы подключенному слоту            
            self.msleep(2000)          # Заставляет текущий поток спать (2000) миллисекунд msecs.
# +++ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

# --->vvvvvvvvvv           vvvvvvvvvvv  vvvvvvvvvvvvv <----------------------------        
class MainWindow(QtWidgets.QMainWindow, Ui_MainWindow):
    def __init__(self):
        super().__init__()

        self.setupUi(self) 

        self.pushButton_2.clicked.connect(self.start_autoswap)
        self.pushButton_3.clicked.connect(self.stop_autoswap)
        self.pushButton_5.clicked.connect(self.reg)
        self.pushButton_4.clicked.connect(self.settings_autoswap)
        
        self.pushButton_2.setEnabled(False)
        self.pushButton_3.setEnabled(False)
        self.pushButton_4.setEnabled(False)

# !!!     
        self.conn = sqlite3.connect('login.db')
        self.cur = self.conn.cursor()  
# !!!         
        self.login = None  # !!! вот тут будет логин, который будет доступен 
                           # !!! в любом окне вашего приложения
        
# +++   self.label        
        self.label = QtWidgets.QLabel(self.groupBox)
        self.label.setGeometry(QtCore.QRect(0, 120, 210, 400))
        self.label.setStyleSheet("font: 12pt \"MS Shell Dlg 2\";\n"
"background-color: rgb(77, 77, 0);"
"color: rgb(255, 55, 55);")
        self.label.setScaledContents(True)
        self.label.setAlignment(QtCore.Qt.AlignCenter)

# "Регистрация/вход"
    def reg(self):                            
        self.reg = SignInUp(self)                                # !!! +++ (self)
        self.reg.show()

    def successfully_logged(self):                               # !!! +++
        self.login = self.reg.login
        s_a = self.cur.execute(
            'SELECT * FROM settings_autoswap WHERE login = ?',
                (self.login,)).fetchone()
        self.label.setText(f'{self.login}\n\n{s_a}')
        
        self.pushButton_2.setEnabled(True)
        self.pushButton_4.setEnabled(True)
        self.settings_autoswap = None

    def settings_autoswap(self):
        if self.settings_autoswap:
            self.settings_autoswap.close()
        self.settings_autoswap = SettingsAutoswap(self)
        self.settings_autoswap.show()

    def start_autoswap(self):
        msg = QMessageBox()
        msg.setIcon(QMessageBox.Information)
        msg.setText("Вы хотите включить автосвап?")
        msg.setWindowTitle("Внимание!")
        msg.setStandardButtons(QMessageBox.Ok | QMessageBox.Cancel)
        retval = msg.exec_()
        if retval == QtWidgets.QMessageBox.Ok:
            self.autoswap()
            
#            self.autoswap_thread = threading.Thread(target=self.autoswap, daemon=True)
#            self.autoswap_thread.start()

    def stop_autoswap(self):
        msg = QMessageBox()
        msg.setIcon(QMessageBox.Information)
        msg.setText("Автосвап выключен!")
        msg.setWindowTitle("Внимание!")
        msg.setStandardButtons(QMessageBox.Ok | QMessageBox.Cancel)
        retval = msg.exec_()
        if retval == QtWidgets.QMessageBox.Ok:
            self.thread.running = False
            self.pushButton_2.setEnabled(True)
            self.pushButton_3.setEnabled(False)        

    def autoswap(self):
        self.thread = Thread(self.login)                                   # !!!
        self.thread.value_changed.connect(self.slot_value_changed)         # !!!
        self.thread.start()                                                # !!!
        self.pushButton_2.setEnabled(False)
        self.pushButton_3.setEnabled(True)

    def slot_value_changed(self, value_changed):
        #print(f'{value_changed}')     
        self.label.setStyleSheet(value_changed) 
        if self.settings_autoswap:
            self.settings_autoswap.label.setStyleSheet(value_changed)

    def closeEvent(self, event):
        self.conn.close()
        event.accept()
        

if __name__ == "__main__":
    import sys
   
    app = QtWidgets.QApplication(sys.argv)
    w = MainWindow()
    w.show()
    sys.exit(app.exec())

Скрипт, который сформирует БД с необходимыми таблицами для тестирования, может выглядеть примерно так:

database.py:

import sqlite3

def createTable():
    connection = sqlite3.connect('login.db')

    connection.execute("CREATE TABLE USERS(USERNAME TEXT NOT NULL,EMAIL TEXT,PASSWORD TEXT)")
    connection.execute("INSERT INTO USERS VALUES(?,?,?)",('admin','[email protected]','admin'))
    connection.commit()

    connection.execute("CREATE TABLE settings_autoswap(login TEXT NOT NULL, coord_X INTEGER, coord_y INTEGER, button INTEGER)")
    connection.execute("INSERT INTO settings_autoswap VALUES(?,?,?,?)",('admin', 333, 333, 3))
    connection.commit()

    result = connection.execute("SELECT * FROM USERS")
    for data in result:
        print("Username : ",data[0])
        print("Email : ",   data[1])
        print("Password :", data[2])

    connection.close()

createTable()