I currently run Plex on my home media server, a long with Plexamp for streaming to my mobile device. Works like a charm.
I've been mostly happy with Plexamp. Main issue with it is the inability to sync my entire music library offline onto my phone (FLAC->Opus) which according to their support pages is not a feature they plan on supporting.
Mediamonkey is pretty good. I held onto media player as long as I could, but MS just made it worse on every iteration.
I’m liking Jellyfin’s music support for my giant collection of FLACs (other formats are supported). I can pull it up on any browser (don’t need to install anything on my work PC). There’s also an iOS app called Fintunes that provides a great native music-listening experience.
Finamp is another iOS app which, importantly for me, supports offline playback via downloading locally.
Does Apple Music (the app) no longer support that? It does on macOS, even without a subscription.
Also, foobar2000 of course.
Apple Music is mostly fine. And as long as you're going to sync to an iPhone, it probably doesn't make sense to use a different app. (Though I use VLC for other things.)