Any way to listen to music (privately?)

I'm going insane. I cannot for the life of me find a suitable way to listen to music privately. I'm on iOS, and I don't know whether to just stick to Apple Music or give up on music in general (I tried, TRIED to go local, but all the apps are shitty). Any way to listen to music and not have your data compromised? Should I just stick to Apple Music and hope that laws change (maybe something like EU's DMA?)

Edit: Hey all! First of all, thank you so much for all the recommendations! I've discovered so many great apps and tools I didn't even know existed (and it has also brought my hopes up for privacy in general). Even though it's still not perfect, I've been using foobar2000 on iOS, downloading music I find (I'm still using Apple Music for discovery, but will probably stop when my subscription ends this month). For desktop I'm using HyperPipe, which although a little buggy at times is so awesome! One thing I do miss about this system is the lack of lyrics. Apple Music has such a beautiful UI when it comes with lyrics, but you can't have it all when it comes to privacy it seems. Thanks for the amazing discussion! I'm so far loving Lemmy ;)