Similar Issue...
We are developing an app that also uses MusicKit. We're able to connect to the Apple service, search and play music, but things go off the rails with a 403 error when we try to get individual user information such as playlists. It seems to be somewhat random, but if you navigate to Apple Music > Account Info and edit "Apps with Access" and remove your app entry, (to try and create a new one..) a new one never seems to be generated even though the requests for access are successful and tokens are returned. Dead in the water as well...