If one end of the connection is a native app like this you have plenty of other options. Browser to browser is the use case I'm talking about.
It could be done with a browser-owned dialog to select peers instead of exposing all local peers to the web by default. Similar to the web MIDI API or others that expose local devices only with explicit user permission for the specific device.
It uses mDNS for discovery. You can only do one browser though.
I don’t see a path forward on browser/browser that is obvious. It would make it so easy to fingerprint if you could set your mDNS hostname in JS