Rethink, for example. Also allows denying an app internet access, if your OS can’t do it by itself.

I also wonder what connections it normally makes and how many)

I wonder what happens if you deny the app internet access? The permission for it is separate from “nearby devices” or “location”. Or use the firewall specifically for it?

Also yeah, the whole situation is messed up, never thought headphones could require an app :/