I see. I don't believe you need to be a paid developer, but I don't have an authoritative source on that I'm afraid. But I believe it will require the users of your client to log in and they need to subscribe to Apple Music and then that's the win on Apple's side, not the API usage you may have.
There is a Linux snap based Apple Music client, though I believe that just basically wraps a web view for music.apple.com
If anyone else knows for certain, please add to this thread; I don't think you need to be a paid developer but am not certain, so a more definitive answer is welcome