I see, that is odd indeed. I am using Blender build 4.2.0, without any additional addons or extensions. I downloaded the last update as well but everything seems to be working on my end, apart for occasionally missing texture paths.
Those missing texture paths will also be fixed with that update. Regardless of that, I have started exporting the models to .obj, so at least there will be a alternative in the future.
However one of my biggest issues is that for some reason unknown to me, those will not link to textures correctly. Those links would have to be set manually by the end-user (i.e. in the Godot-Inspector), which is tedious to do for 250+ models to say the least.
Edit: Nevermind, the issue of the textures not getting correctly linked to the meshes only seems to appear for .fbx files. Since its only an issue with those and it works very well with .obj I will put my priorities on .obj files.