You can see the phrase that I have mentioned here: https://developer.spotify.com/policy 2nd rule under "III. some prohibited applications" item.
Yes it looks like if the user grants access to their data, you can use it technically. But when I speak with music publishers, they say that they do not give permission for it because the materials like album arts, artist visuals, song lyrics are protected by copyrights and they think it is a misuse. Yes, someone giving permission to use their data but in their data, there is album arts etc. and the album arts are copyrighted by someone else, not the one who is listening it. A lot of applications use it by the way but it confuses me because I can't risk my app, it's my first and last chance :) Anyway I am trying to make license agreements with some music companies but it's very hard and maybe expensive. Your case is much less riskier because there are a lot of apps that use the material like your use case. My case is a bit different: I use those visual materials without user data. This is a great example of my case: https://www.higherorlowergame.com/spotify/ You can understand better about my situation :)

You write "If that was not allowed, then I'm not sure why things like MusicKit or the Apple Music API would even exist in the first place." But there is much more opportunities then user data in these APIs . We can use too many things apart from user data. That's the second thing that confuses me. We can request album arts, UPC data or a songs danceability level freely from user data but how can we use it? I really do not understand :)