d'Ivan

for label, callback in self.menu_items.items():
            menu_item = Gtk.MenuItem(label)
            menu_item.connect("activate", lambda _: callback())
            self.menu.append(menu_item)

        self.menu.show_all()
        self.indicator.set_menu(self.menu)

    def open_app(self, _):
        # Add your app's functionality here
        win = Gtk.ApplicationWindow(application=app)
        btn = Gtk.Button(label="Hello, World!")
        btn.connect('clicked', lambda x: win.close())
        win.set_child(btn)
        win.present()
        #print("Opening the app")

for label, callback in self.menu_items.items():
            menu_item = Gtk.MenuItem(label=label)
            menu_item.connect("activate", callback)
            self.menu.append(menu_item)

        self.menu.show_all()
        self.indicator.set_menu(self.menu)

        self.application = Gtk.Application()
        self.application.connect('activate', self.on_activate)
        self.application_window = None

    def open_app(self, _):
        # Add your app's functionality here
        self.application.register(None)  # Регистрация приложения
        self.application.activate()      # Активация приложения

    def on_activate(self, app):
        if not self.application_window:
            self.application_window = Gtk.ApplicationWindow(application=app)
            btn = Gtk.Button(label="Hello, World!")
            btn.connect('clicked', lambda x: self.application_window.close())
            self.application_window.add(btn)
            self.application_window.show_all()
        else:
            self.application_window.present()

for label, callback in self.menu_items.items():
            menu_item = Gtk.MenuItem(label=label)
            menu_item.connect("activate", callback)
            self.menu.append(menu_item)

        self.menu.show_all()
        self.indicator.set_menu(self.menu)

        self.application = Gtk.Application()
        self.application.connect('activate', self.on_activate)
        self.application_window = None

    def open_app(self, _):
        # Add your app's functionality here
        if not self.application_window:
            self.application.register(None)
        self.application.activate()

    def on_activate(self, app):
        if not self.application_window:
            self.create_window(app)
        else:
            self.application_window.present()

    def create_window(self, app):
        self.application_window = Gtk.ApplicationWindow(application=app)
        self.application_window.set_title("My System Tray App")
        self.application_window.set_default_size(200, 200)
        self.application_window.connect("delete-event", self.on_window_close)

        btn = Gtk.Button(label="Hello, World!")
        btn.connect('clicked', lambda x: self.application_window.hide())  # скрываем окно вместо закрытия
        self.application_window.add(btn)
        self.application_window.show_all()

    def on_window_close(self, window, event):
        self.application_window = None  # устанавливаем в None для воссоздания окна в следующей активации
        window.destroy()
        return True  # значит, уже обработали событие