Как отловить нажатие левой клавиши мыши на Linux вне виджета PyQt5?

Как вариант:
pynput.mouse содержит классы для управления и наблюдения за мышью.

from PyQt5 import QtCore, QtGui, QtWidgets
from PyQt5.QtWidgets import QWidget, QApplication, QLabel, QVBoxLayout, QPushButton
from PyQt5.QtCore    import Qt, QTimer

from pynput import mouse                                       # pip install pynput


class Ui_Form(object):
    def setupUi(self, Form):
        Form.setObjectName("Form")
        Form.resize(171, 122)
        Form.setMaximumSize(QtCore.QSize(512, 512))
        Form.setMinimumSize(QtCore.QSize(512, 512))
        Form.setStyleSheet("")                          
        Form.setWindowFlags(QtCore.Qt.FramelessWindowHint | QtCore.Qt.WindowStaysOnTopHint)

        self.Clicker = QtWidgets.QLabel(Form)
        self.Clicker.setGeometry(QtCore.QRect(0, 0, 512, 512))
        self.Clicker.setText("")
        self.Clicker.setPixmap(QtGui.QPixmap("lena.jpg"))
        self.Clicker.setScaledContents(True)
        self.Clicker.setObjectName("Clicker")
        self.Status = QtWidgets.QLabel(Form)
        self.Status.setGeometry(QtCore.QRect(10, 40, 61, 61))
        self.Status.setText("")
        self.Status.setPixmap(QtGui.QPixmap("Ok.png").scaled(61, 61))
        self.Status.setObjectName("Status")
        self.Numb = QtWidgets.QLabel(Form)
        self.Numb.setGeometry(QtCore.QRect(80, 20, 181, 101))
        self.Numb.setStyleSheet("color:#f00;\n"
"font: 87 45pt \"Arial Black\";")
        self.Numb.setScaledContents(True)
        self.Numb.setObjectName("Numb")

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

    def retranslateUi(self, Form):
        _translate = QtCore.QCoreApplication.translate
        Form.setWindowTitle(_translate("Form", "Form"))
        self.Numb.setText(_translate("Form", "0"))


class ButtonReleaseManager(QtCore.QObject):
    clicked = QtCore.pyqtSignal(int, int)

    def __init__(self, parent=None):
        super().__init__(parent)
        self._listener = mouse.Listener(on_click=self._handle_click)
        self._listener.start()

    def _handle_click(self, x, y, button, pressed):
        if pressed and button==mouse.Button.left:
            self.clicked.emit(x, y)
        
        
class Window(QtWidgets.QWidget, Ui_Form):
    def __init__(self):
        super().__init__()
        self.setupUi(self)
        
        self.old_pos = None
        self._click = 0              
        self._all_click = 0        

        self.manager = ButtonReleaseManager()          
        self.manager.clicked.connect(self.allClicked) 
        
    def allClicked(self):                           
        self._all_click  += 1    
        QtCore.QTimer.singleShot(15,                            
            lambda: self.Numb.setText(f"{self._all_click - self._click}")) 

    def mousePressEvent(self, event):         
        if event.button() == Qt.LeftButton:
            self.old_pos = event.pos()
            self._click += 1              

    def mouseReleaseEvent(self, event):
        if event.button() == Qt.LeftButton:
            self.old_pos = None

    # вызывается всякий раз, когда мышь перемещается
    def mouseMoveEvent(self, event):
        if not self.old_pos:
            return
        delta = event.pos() - self.old_pos
        self.move(self.pos() + delta)        
        

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

lena.jpg

Ok.png