I haven’t heard about this kind of module for Godot. But it would be possible write them if you are familiar with Android live wallpapers sdk (or windows screen-savers one).
Godot is not really designed with this in mind - it might use more CPU/GPU resources than if you wrote it using a simpler rendering engine, not to mention the longer start-up time.
I can tell you, at least about the windows screensavers, that it should be possible. Windows Screensavers are just .exe files renamed to a .scr ending. So if you export a godot project to an executable .exe file and rename it poperly, it shouldn’t be a problem.
Android live wallpapers are another thing and I don’t know, how they work at all, so I can’t tell you.