Popups don't register mouse click shortly after opening

[mihe]

Tested versions

Reproducible in: 4.3.rc [86c95d2]
Reproducible in: 4.3.rc [5e7592a]
Not reproducible in: 4.3.rc [031b71f]

System information

Windows 11 (10.0.22631)

Issue description

This seems to be a regression between 4.3-RC2 and 4.3-RC3, stemming from #95232.

When opening pretty much any popup in Godot, like the window top menu, or a context menu, and then releasing the mouse button and clicking somewhere in the popup within a short timeframe (presumably 400 ms) that second mouse click doesn't seem to register.

TopMenu.mp4

ContextMenu.mp4

Lowering the timeout changed in #95232 back to 150 ms seems to resolve the regression.

Steps to reproduce

1. Open the editor
2. Click one of the items in the top window menu
3. Quickly click the first item in the menu
4. Note how the click doesn't register

Minimal reproduction project (MRP)

N/A

[Calinou]

I can't reproduce this on:

Godot v4.3.rc (39fc116) - Fedora Linux 40 (KDE Plasma) - X11 - Vulkan (Forward+) - dedicated NVIDIA GeForce RTX 4090 (nvidia; 555.58.02) - 13th Gen Intel(R) Core(TM) i9-13900K (32 Threads)

Single-window mode is disabled in the editor settings. This may be Windows-specific.

[mihe]

As mentioned in #95432 I am similarly not able to reproduce this issue on Linux, but I am able to reproduce it on macOS (and Windows of course), and #95432 seems to resolve the problem on both affected platforms.