I remember some of the malarkey done with the X11 SHAPE extension. There was a program called xmascot. You could give it an xpm of a character or use one of the presets—typically a cute animal of some sort or a chibi anime waifu. It would show a dangling figurine of this character right on your desktop, autogenerating a few frames of rotation so it could swing from side to side.

Of course X11 is four olds, and there's probably some security justification for not having nonrectangular windows in Wayland, and/or "that's a compositor implementation detail and outside the scope of the Wayland protocol".