Iconsistent close_requested emission with FLAG_POPUP

[Summersay415]

Tested versions

• Reproducible in v4.3.dev6.official [64520fe]
• Reproducible in v4.2.2.stable.official [15073af]
• Partially reproducible in v4.1.4.stable.official [fe0e8e5]
• Partially reproducible in v4.0.4.stable.official [fc0b241]

System information

Godot v4.3.dev6 - Ubuntu 24.04 LTS 24.04 - X11 - GLES3 (Compatibility) - Mesa Intel(R) Graphics (ADL GT2) () - 12th Gen Intel(R) Core(TM) i5-1235U (12 Threads)

Issue description

There is some inconsistency with close_requested signal emission with enabled embed_subwindows and disabled.
We have three windows: one Window, one AcceptDialog, one PopupPanel, everything with popup_window enabled and exclusive disabled.
Behavior with embed_subwindows disabled:

• Window: when clicked outside or close button pressed, emits close_requested (twice if version >4.2 and Linux/*BSD).
• AcceptDialog: when clicked outside or close button pressed, emits close_requested and canceled (both twice if >4.2 and Linux/*BSD). When clicked on OK, (emits canceled and close_requested - if >4.2 and Linux/*BSD) and emits confirmed.
• PopupPanel: when clicked outside, emits close_requested (twice if >4.2 and Linux/*BSD) and popup_hide.

It strangely changes when embed_subwindows is enabled:

• Window: when clicked outside, does nothing... If close button pressed, emits close_requested (correct).
• AcceptDialog: when clicked outside, emits only canceled AND closes. When clicked on OK, emits both canceled and confirmed, but not close_requested. If close button pressed, emits canceled and close_requested.
• PopupPanel: when clicked outside, emits only popup_hide AND closes.

Related to: #85417

Steps to reproduce

1. Download MRP.
2. Do steps described higher.
3. Observe result by looking at console.

Minimal reproduction project (MRP)

mrp.zip

[Summersay415]

Bisected when double emission started:

8c1ce404d7d96c7034018a37cbf4a8bcad6d7386 is the first bad commit
commit 8c1ce404d7d96c7034018a37cbf4a8bcad6d7386
Author: Markus Sauermann <6299227+Sauermann@users.noreply.github.com>
Date:   Wed Aug 2 00:17:25 2023 +0200

    Fix crash on Windows when closing `Window`
    
    Send `WINDOW_EVENT_MOUSE_EXIT` when a window is destroyed.
    
    Ensure, that on Windows, the event_callback is still valid during
    destroying the `Window`.

 platform/linuxbsd/x11/display_server_x11.cpp | 6 ++++++
 platform/windows/display_server_windows.cpp  | 4 ++++
 scene/main/window.cpp                        | 6 ------
 3 files changed, 10 insertions(+), 6 deletions(-)

PR: #80142