As I mentioned, is it not possible to provide an in-app experience (and not take the user to the Apple Music app)?

Apologies for the late reply. I hope you've figured it out. If not, you can take advantage of the Playlist relationship endpoint and provide tracks as the relationship. It provides you with all the tracks. Example: https://api.music.apple.com/v1/catalog/us/playlists/pl.f4d106fed2bd41149aaacabb233eb5eb/tracks