44.rc: breaks Fullscreen mode on most SDL based games (Ren'Py, Unity, FNA, Source-Engine, ...) running through X/Xwayland

Affected version

Fedora 38
44~rc-2.fc38
Wayland

Bug summary

On most Ren'Py (visual novel engine) games Gnome 44 introduced a short flicker on entering/leaving fullscreen mode.
With 44.rc a few breaking issues appeared depending on the game/Ren'Py (engine) version:

1. Most games will flicker into Fullscreen mode and then disappear completly (the games are still running and their process seem healthy, but their window is nowhere to be found)
2. On some games switching into Fullscreen mode leads to an endless loop of entering/leaving (the log is filled with The window was minimized. <-> The window was restored.
3. On a lot of games the game tries to go fullscreen (the turning fullscreen animation of mutter is shown), but the game stays windowed in its original size without a title bar.

Steps to reproduce

The breaking issue (1) can be reproduced with the free game "Don't Forget Our Esports Dream" on Steam.

1. Install https://store.steampowered.com/app/946560/Dont_Forget_Our_Esports_Dream/ from Steam
2. Start the game until the main menu is seen
3. Try to enter fullscreen mode using F11
4. The window will either flicker and turn weird, or turn invisible. A few tries might be needed to see 1) instead of 3).
5. As the game remembers the last mode it was closed in it will start invisible on next boot.