There is some ongoing PR, so it might come at some point :

https://github.com/godotengine/godot/pulls?q=is%3Apr+is%3Aop...

> Just the other day I was wondering - what would it take to develop a Linux WM in Godot?

It bas been done :

https://github.com/SimulaVR/gdwlroots

But it is not up to date with Godot 4. You can have your Firefox or Blender window be a regular texture inside a full Godot game, pretty crazy...

This is sadly just a nested compositor, it seems like it does not implement any new Godot drivers…