как в React удалить элемент

Добавить key={} надо было для каждого элемента списка. Вы не там его добавили изначально.

import React from "react";

class List extends React.Component {
  constructor(props) {
    super(props);
    this.state = {
      type: props.type,
      items: props.items
    };
  }

  remove(id) {
    console.log(id);
    this.setState({
      items: this.state.items.filter((el) => el.id !== id)
    });
  }

  render() {
    return (
      <div className="row d-flex flex-row align-items-center justify-content-center w-100 h-100 overflow-auto m-0 h-auto">
        {this.state.items.map((item) => (
          <Items key={item.id} item={item} remove={this.remove.bind(this)} />
        ))}
      </div>
    );
  }
}

class Items extends React.Component {
  constructor(props) {
    super(props);

    this.setName = this.setName.bind(this);
    this.setContent = this.setContent.bind(this);
    this.setDate = this.setDate.bind(this);

    this.state = {
      id: this.props.item.id,
      name: this.props.item.name,
      content: this.props.item.content,
      date: this.props.item.date,
      type: props.item.type,
      isNew: props.item.isNew
    };
  }

  setName(e) {
    this.setState({ name: e.target.textContent.slice(0, 50) });
    setTimeout(() => this.afterSet(), 0);
  }

  setContent(e) {
    this.setState({ content: e.target.textContent.slice(0, 1000) });
    setTimeout(() => this.afterSet(), 0);
  }

  setDate(e) {
    this.setState({ date: e.target.text });
    setTimeout(() => this.afterSet(), 0);
  }

  afterSet() {
    $.post('/toDoSave', this.state, (data) => {
        if (data.isNew) {
            this.setState({id: data.id, isNew: false})
        }
    })ж
  }

  render() {
    return (
      <div className="item container">
        <div
          contentEditable={true}
          placeholder={"Имя"}
          className="note-name border-bottom border-1 m-2 d-flex align-items-center outline-none my-text text-break overflow-auto"
          onBlur={this.setName}
        >
          {this.state.name}
        </div>

        <div
          contentEditable={true}
          placeholder={"Текст"}
          className="note-content border-1 m-2 outline-none my-text overflow-auto text-break my-scroll"
          onBlur={this.setContent}
        >
          {this.state.content}
        </div>
        <div className="note-button-group m-2 border-top border-1 d-flex flex-row align-items-center justify-content-between">
          <div className="d-flex flex-row">
            <div className="note-button p-2 ms-1">
              <i className="fa-solid fa-chart-bar"></i>
            </div>
          </div>
          <div className="d-flex flex-row">
            <div className="note-button p-2 ms-1">
              <i className="fa-solid fa-circle-exclamation"></i>
            </div>
          </div>
          <div className="d-flex flex-row">
            <div className="note-button p-2 ms-1">
              <i className="fa-solid fa-calendar-days"></i>
            </div>
            <div
              className="note-button p-2 ms-1"
              onClick={() => {
                this.props.remove(this.props.item.id);
              }}
            >
              remove
              <i className="fa-solid fa-trash-can"></i>
            </div>
            <hr />
          </div>
        </div>
      </div>
    );
  }
}

export default function App() {
  return (
    <List
      items={[
        {
          id: 1,
          name: "name1",
          content: "namdse1",
          date: new Date(),
          type: "name1",
          isNew: false
        },
        {
          id: 2,
          name: "name2",
          content: "namdse2",
          date: new Date(),
          type: "name2",
          isNew: false
        },
        {
          id: 3,
          name: "name3",
          content: "namdse3",
          date: new Date(),
          type: "name3",
          isNew: false
        }
      ]}
    />
  );
}

P.S. Используйте функциональные компоненты если можно, будет выглядеть читабельнее.