Errors when opening dialog from manually sent close notification

[rhofour]

Tested versions

Reproducible in (at least): 4.3, 4.4dev2, and 4.4dev7

I get the same behavior with both C# and GDscript

System information

Linux (Fedora 41 using Gnome)

Issue description

Motivation: When the user closes my application I would like to open a dialog prompting them to save if content was modified.

Issue:
When I listen for NOTIFICATION_WM_CLOSE_REQUEST and show a dialog this works as expected. However, if I manually trigger the same notification from a button or menu (using get_tree().root.propagate_notification) instead I get the following error:

E 0:00:01:0786   popup_repro.gd:11 @ _notification(): Parent node is busy setting up children, `add_child()` failed. Consider using `add_child.call_deferred(child)` instead.
  <C++ Error>    Condition "data.blocked > 0" is true.
  <C++ Source>   scene/main/node.cpp:1572 @ add_child()
  <Stack Trace>  popup_repro.gd:11 @ _notification()
                 popup_repro.gd:5 @ <anonymous lambda>()

This is similar to #34157 except I don't see the error when the close notification is sent from the window manager.

If I replace cd.popup_exclusive_centered(self) with cd.popup_exclusive_centered.call_deferred(self) this works as expected, but it's not clear why this should be necessary.

Steps to reproduce

1. Open repro project
2. Click the button
3. Observe error

Minimal reproduction project (MRP)

popup-repro.zip

Attached is a tiny repro project, the only code of which is repeated here:

extends Control

func _ready() -> void:
	get_tree().set_auto_accept_quit(false)
	$Button.pressed.connect(func(): get_tree().root.propagate_notification(NOTIFICATION_WM_CLOSE_REQUEST))

func _notification(what: int) -> void:
	if (what == NOTIFICATION_WM_CLOSE_REQUEST):
		var cd = ConfirmationDialog.new()
		cd.get_ok_button().pressed.connect(func(): get_tree().quit())
		cd.popup_exclusive_centered(self)