Self-hosted ( if you want that ) but not P2P: https://about.mattermost.com/
Problem still stands, when your self-hosted instance/software goes down, I still can't communicate with people sitting literally meters away from me, connected to the same WiFi. It's incredibly stupid.
P2P networks can also work even if you're not connected to the same network. Point being that it's a direct connection to the person that you're communicating with, with no indirection.
That doesn't seem like a problem that software can solve.
* At one point we had to re-login to the client, because our ssl cert expired (let's encrypt), I think.
These issues might be because we ran the server from a home internet connection, but I run a lot of things from home without issue.