@tarkowski You never got a good answer, so I'll pick this up.
The most significant example of a Fedi server with unique functionality and community is probably friend.camp, run by @darius .
He forked Mastodon to create Hometown, which has features like local-only posting to strengthen the local community. He has also built other services around Hometown/Mastodon, which tie into the community and the user identity and offer other features, federated or not.
Finally, the onboarding process is slow, personal and deliberate, in contrast with the instant open registration of big general-purpose servers.
Here is his talk and the subsequent Q&A (both hosted on PeerTube, of course) from 2020's apconf: