Python Gtk: How to use the same widget on different pages of the same notebook?

No, a widget can only have one parent at a time. If you want the same controls to appear on all pages of the tab, you'll have to either create duplicate controls, dynamically move them when tab pages are changed, or put them outside the tab control entirely.

Moving controls around is done by calling remove() on the old parent and add() (or a control-specific variant, such as push_start()) on the new parent. (I forget if you need to manage reference counts in Python; if so, you also have to ref() the widget being moved first and unref() it later; otherwise, remove() will destroy the widget.)

You can follow this tutorial within pyGObject and python3 in order to solve your issue.

Try, to follow each step:

# This is a test application within PyGObject version 3.0+
import gi
# Test if gi version is 3.0+ 
gi.require_version('Gtk', '3.0')

from gi.repository import Gtk

class TestNoteBook(Gtk.Window):
    def __init__(self):
        # Initialize Gtk.Window
        Gtk.Window.__init__(self)
        # Add title to this app
        self.set_title("Test Note Book")
        # Connect the close button to self.quit_app() method
        self.connect("delete-event", self.quit_app)

        # Create a new Gtk.Widget with type Gtk.Notebook()
        notebook = Gtk.Notebook()
        # Add notebook to the current app class
        self.add(notebook)
        # Create a Gtk.HBox() in which we can add widgets
        page1 = Gtk.HBox()
        # Create button1
        button1 = Gtk.Button("I'm in the page 1")
        # Connect button1 to a signal
        button1.connect("clicked", self.button_clicked, "button1")
        # Add a Button to page1
        page1.add(button1)
        # Add page1 to the notebook with label page-1
        notebook.append_page(page1, Gtk.Label("page-1"))
        # Create new Gtk.HBox()
        page2 = Gtk.HBox()
        # Create button2
        button2 = Gtk.Button("I'm in the page 2")
        # Add a signal to button2
        button2.connect("clicked", self.button_clicked, "button2")
        # Add a button to page2
        page2.add(button2)
        # Add pag2e to the notebook with label page-2
        notebook.append_page(page2, Gtk.Label("page-2"))

    def run(self):
        # Show all the widgets
        self.show_all()
        # Run the Gtk.main loop
        Gtk.main()

    def quit_app(self, widget, args):
        # Print a message with the ID of the widget and its argument
        print("Exit this current window...", widget, args)
        # Exit from the window
        Gtk.main_quit()

    def button_clicked(self, widget, args):
        if args == "button1":
            print("Button 1 clicked!")
        else:
            print("Button2 clicked!")


# test
if __name__ == '__main__':
    app = TestNoteBook()
    app.run()