It'd be nice if it were possible to set capes in addition to skins by using /cape. If I were to open a pull request for this, would you be interested?

Sounds interesting, but I don't think capes are possible to implement server-side?

I don't have much experience with java, but I'll read up on the Fabric API and see what I can do. In the meanwhile, I've found a Forge mod that allows setting the cape and can be run on servers: SkinChanger.

Humm, I've checked out the source but at the first glance I don't really get how cape loading works :).

However, it is strange to me that there's no cape plugin for bukkit / spigot /paper ...

Yeah, I got nothing on my end. While I understand more or less how your mod works, I don't understand how the other one sets the Cape.