Very interesting, thanks! Is it possible for people to register on that relay?

(if I understand correctly) you don’t register on a relay, you register on a PDS (which you can easily self-host on a small computer at home). But, to register with a PDS, you need a DID, and to interoperate with the rest of bluesky it needs to be using one of their two currently-supported DID methods: either did:web or did:plc. The former is a thing which you can create using a domain you control, which gives you an identity that you lose control of when you lose control of that domain. The latter is the actually-centralized “placeholder” DID method implemented by an append-only log operated by BlueSky PBC, which is what most people are actually using. I’m not sure if/how you can create a did:plc without first creating an account on a bsky.app PDS, but you can migrate it to your own PDS after creating one there. or, you can use did:web and rely on your domain name registration instead of their centralized log.

Further reading:

• How to self-host all of Bluesky except the AppView (for now) (from November last year)
• minimal AppView example
• “self-hosting entire bluesky” with docker-compose (including AppView, apparently)