I have seen this for some time when manually sync'ing an iPhone pre Catalina and it got way worse after Catalina with the Music app, exactly as you describe even up to 10 duplicates in one case. After starting to use the Apple Music service I enabled Sync Library and the playlist duplication has not occurred with that (just different issues). So it may not be Apple Music that's doing it but the Music app under Catalina when manually sync'ing a phone. There's not much you can do to solve the issue other than keep deleting the duplicates of both your mac and your phone and keep reporting it to the trillion dollar mothership.
As for Apple Music messing with your library - if you go the Sync Library route, yes, the process has many issues but I have not "lost" anything and is stable now. There are many threads on here about libraries getting messed up. If you are going to enable Sync Library I would suggest backing it up first.