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https://listenbrainz.org/ is open source (from the MusicBrainz ppl), though not really intended for self-hosting.

You can import your Last.fm history over to ListenBrainz too. Most of the 'scrobbling' apps will work with ListenBrainz also.

I believe FunkWhale is attempting something along these lines: https://fediverse.party/en/funkwhale/