[4.0] Game debug window sometimes opens behind the Godot editor (DisplayServer regression)

[PrecisionRender]

Godot version

v4.0.alpha.calinou [9d1626b]

System information

Windows 11, Vulkan, Nvidia GeForce RTX 2060 Max-Q

Issue description

When testing a game by clicking the play button in the Godot editor, the window will sometimes open behind the Godot editor. I have been unable to find a consistent way to reproduce this, although it does seem to happen more often after the first time a scene is run. It seems to hardly ever happen if the scene's root is just a Node.

I have changed many different window settings, and none seemed to affect this problem, except for Always on top.

Steps to reproduce

Unkown: it seems to happen on its own.

Minimal reproduction project

No response

[Calinou]

Related to #57152.

@PrecisionRender Can you reproduce this after enabling Single Window Mode in the Editor Settings then restarting the editor?

[PrecisionRender]

@Calinou No. That seems to keep the issue from happening, at least from testing it for 2 minutes.

[mhilbrunner]

It seems this may have been caused by f4ea9cd (merged in PR #57341).
Thats the earliest commit I can reproduce it with, the one immediately before (29c4644) seems unaffected.

I can reproduce this pretty consistently with a larger project that takes some time to initialize/run.

[bruvzg]

It seems this may have been caused by f4ea9cd (merged in PR #57341).

Is it reproducible after #57961?
Also, is it reproducible with versions before #57341, if you toggle editor full-screen on and off before running the project?