FINALLY I am manually synchronizing MY music library, which has grown a lot over the past 20+ years, with my iPhone NOT using the paid music service Apple Music - which only syncs music they also own. Not all of your music.
I needed to plug my iPhone via USB-C cable directly into my Mac Mini to be recognized by the Mac.
Liberating my music feels so great :-) ...
@andreas_heitmann i did it the other way round, added music to iTunes, then it syncs it iCloud via iTunes Match - even music it does not know.
@Berndlackinger The sync didn't work well for me though. When syncing via USB-C cable everything is just fine, as it should be ...