Как мне перетянуть данные полученные с класса Background функции post_background в класс Window(а точнее в функцию get_background)?

я отметил для вас строки, который я поменял:

import sys
from PyQt5.Qt import *


class Background(QDialog):
    background_bottom = ''
    background_top = ''

    def __init__(self):
        super().__init__()

        self.width = 400
        self.height = 400
        self.title = 'Background'

        self.init_window()
        self.center()
        self.init_ui()
        self.show()

    def init_window(self):
        self.setGeometry(0, 0, self.width, self.height)
        self.setWindowTitle(self.title)

    def center(self):
        qtRectangle = self.frameGeometry()
        centerPoint = QDesktopWidget().availableGeometry().center()
        qtRectangle.moveCenter(centerPoint)
        self.move(qtRectangle.topLeft())

    def init_ui(self):
        root_layout = QVBoxLayout()
        self.combobox = QComboBox()
        self.combobox.addItem('Contrast')
        self.combobox.addItem('Monako')
        root_layout.addWidget(self.combobox)
        background_label = QLabel('background')
        background_label.setAlignment(Qt.AlignCenter)
        root_layout.addWidget(background_label)
        buttons_layout = QHBoxLayout()
        buttons_layout.setAlignment(Qt.AlignRight)
        button_ok = QPushButton('Ok')
        button_ok.clicked.connect(self.post_background)
        button_cancel = QPushButton('Cancel')
        button_cancel.clicked.connect(self.cancel)
        buttons_layout.addWidget(button_ok)
        buttons_layout.addWidget(button_cancel)
        root_layout.addLayout(buttons_layout)
        self.setLayout(root_layout)
# >>
    def post_background(self):
        background = self.combobox.currentText()
        if background == 'Contrast':
            self.background_top = 'white'
            self.background_bottom = 'black'
        elif background == 'Monako':
            self.background_top = 'black'
            self.background_bottom = 'yellow'
        self.close()                               

        #print(f'def post_background(self): \n{self.background_top}, \n{self.background_bottom}')

        return self.background_top, self.background_bottom

    def cancel(self):
        self.close()


class Window(QMainWindow):
    buffered_text = ''
    current_text = ''
    count = 1
    text_after = ''
    text_before = ''
    text_copy = ''
    isSaved = False

    def __init__(self):
        super().__init__()

        self.top = 150
        self.left = 150
        self.height = 600
        self.width = 1200
        self.default = 'Simple'
        self.title = f'{self.default}-Notebook'

        self.init_ui()
        self.init_window_1()
        self.show()

    def init_ui(self):
        self.textbox = QTextEdit()
        self.textbox.setFocusPolicy(Qt.StrongFocus)
        self.textbox.setFont(QFont('Times', 18))
        self.textbox.selectionChanged.connect(self.handleSelectionChanged)
        self.cursor = self.textbox.textCursor()

        bar = self.menuBar()
        file_menu = bar.addMenu('File')

        create_action = QAction('Create', self)
        create_action.setShortcut('CTRL+N')
        open_action = QAction('Open...', self)
        open_action.setShortcut('CTRL+O')
        save_action = QAction('Save', self)
        save_action.setShortcut('CTRL+S')
        save_as_action = QAction('Save as...', self)
        save_as_action.setShortcut('CTRL+SHIFT+S')
        close_action = QAction('Close', self)

        file_menu.addAction(create_action)
        file_menu.addAction(open_action)
        file_menu.addAction(save_action)
        file_menu.addAction(save_as_action)
        file_menu.addSeparator()
        file_menu.addAction(close_action)

        create_action.triggered.connect(self.create)
        open_action.triggered.connect(self.open)
        save_action.triggered.connect(self.save)
        save_as_action.triggered.connect(self.save_as)
        close_action.triggered.connect(self.close_app)

        file_edit = bar.addMenu('Edit')

        cancel_action = QAction('Cancel', self)
        cancel_action.setShortcut('CTRL+Z')
        cut_action = QAction('Cut', self)
        cut_action.setShortcut('CTRL+X')
        copy_action = QAction('Copy', self)
        copy_action.setShortcut('CTRL+C')
        paste_action = QAction('Paste', self)
        paste_action.setShortcut('CTRL+V')
        delete_action = QAction('Delete', self)
        delete_action.setShortcut('DELETE')

        file_edit.addAction(cancel_action)
        file_edit.addSeparator()
        file_edit.addAction(cut_action)
        file_edit.addAction(copy_action)
        file_edit.addAction(paste_action)
        file_edit.addAction(delete_action)

        cancel_action.triggered.connect(self.cancel)
        cut_action.triggered.connect(self.cut)
        copy_action.triggered.connect(self.copy)
        paste_action.triggered.connect(self.paste)
        delete_action.triggered.connect(self.delete)

        file_format = bar.addMenu('Format')

        font_action = QAction('Fonts...', self)
        color_action = QAction('Color', self)
        background_action = QAction('Background', self)

        file_format.addAction(font_action)
        file_format.addAction(color_action)
        file_format.addAction(background_action)
        font_action.triggered.connect(self.get_fonts)
        color_action.triggered.connect(self.get_color)
        background_action.triggered.connect(self.get_background)

        self.setCentralWidget(self.textbox)

    def get_background(self):
#        Background().exec_()
#        background = Background.post_background()

        self.background = Background()                                                      # +++
        self.background.exec_()                                                             # +++
        background = self.background.post_background()                                      # +++

        print(f' background_top = {background[0]} \nself.background_bottom = {background[1]}')                                      # не то!!!!

    def get_fonts(self):
        font, ok = QFontDialog.getFont()
        if ok:
            self.textbox.setFont(font)

    def get_color(self):
        color = QColorDialog.getColor()
        self.textbox.setTextColor(color)

    def init_window_1(self):
        self.setGeometry(self.left, self.top, self.width, self.height)
        self.setWindowTitle(self.title)
        self.setWindowIcon(QIcon('../Icon/Windows_Notepad_Icon.png'))

    def handleSelectionChanged(self):
        text = self.textbox.textCursor().selectedText()

        text = '\n'.join(text.split())

        return text

    def cancel(self):
        print(self.buffered_text)
        print(self.current_text)
        self.current_text = self.textbox.toPlainText()
        self.textbox.setText(self.buffered_text)
        self.cursor.setPosition(len(self.buffered_text), QTextCursor.KeepAnchor)
        self.textbox.setTextCursor(self.cursor)
        self.buffered_text = self.current_text

    def cut(self):
        text = self.handleSelectionChanged()
        self.current_text = self.textbox.toPlainText()
        # print(type(self.current_text))
        print(f'current_text = \n`{self.current_text}`\n')
        self.buffered_text = self.current_text
        if text in self.current_text:
            new_text = self.current_text.replace(text, '')
            self.textbox.setText(new_text)
            self.cursor.setPosition(len(new_text), QTextCursor.KeepAnchor)
            self.textbox.setTextCursor(self.cursor)

    def copy(self):
        self.text_copy = self.textbox.toPlainText()

    def paste(self):
        self.textbox.setText(self.text_copy)

    def delete(self):
        self.cut()

    def save_as(self):
        file_name, _ = QFileDialog.getSaveFileName(self, 'Save', '*.txt', "Текстовые документы (*.txt);;"
                                                                          "All Files()")
        if file_name:
            with open(file_name, 'w+') as file:
                file.write(self.textbox.toPlainText())

    def save(self):
        self.text_before = self.textbox.toPlainText()
        if self.text_before:
            if self.text_before != self.text_after:
                self.save_as()
                self.isSaved = True
                self.text_after = self.text_before

    def open(self):
        file_name, file_extension = QFileDialog.getOpenFileName(self, 'Open file...', 'C://Program Files/')
        if file_name:
            with open(file_name, 'r') as file:
                self.textbox.setText(file.read())

    def create(self):
        text = self.textbox.toPlainText()
        if text:
            change = QMessageBox.question(self, 'Notebook', 'Do you want to save the changes to a file?',
                                          QMessageBox.Save | QMessageBox.No | QMessageBox.Cancel)
            if change == QMessageBox.Save:
                self.save_as()
            elif change == QMessageBox.No:
                self.textbox.clear()

    def close_app(self):
        text = self.textbox.toPlainText()
        if text:
            if not self.isSaved:
                change = QMessageBox.question(self, 'Notebook', 'Do you want to save the changes to a file?',
                                              QMessageBox.Save | QMessageBox.No | QMessageBox.Cancel)
                if change == QMessageBox.Save:
                    self.save_as()
                elif change == QMessageBox.No:
                    sys.exit()
                else:
                    return True

    def closeEvent(self, event):
        if self.close_app():
            event.ignore()
        else:
            self.close_app()

if __name__ == '__main__':
    app = QApplication(sys.argv)
    mywin = Window()
    mywin.show()
    sys.exit(app.exec_())