Yes you can self host the relay server (and please do so!). If you are like me and already have Mac Mini in a closet running docker, k3s, or just have a friend group kubernetes cluster, you can get it running in about 3 minutes.

https://happy.engineering/docs/guides/self-hosting/

https://github.com/slopus/happy-server

There is a Dockerfile, plus a docker-compose.yaml, and a complete Kubernetes template as well.