It didn’t change the repo. F-droid has always slower updates, because they’re compiling every app themselves. Izzy is release directly from app developer, so it’s newer. I’d stick to F-droid, so app dev can’t push anything malicious in the official app build.

Readme on the repo says it’s just scrobbling and fetching metadata. But afaik you can make instant mixes based on this data.

Here’s some tool to sync last.fm playlists to jellyfin: https://soundiiz.com/tutorial/sync-lastfm-with-jellyfin

I don’t think there is any self-hosted server that has a good playlist generation and is fully local, because it would need someone to classify the music in order to work. You can try to connect it to last.fm. I think Jellyfin has the addon for it.