At the moment when you set the App identifier on the Apple Developer web portal you can't check MusicKit as its capability.
At first I thought that it is no longer needed as I made some progress and could authorise the app to use MusicKit on device.
However whenever it tries to access something I get:
[DataRequesting] Failed retrieving tokens for MusicDataRequest.Context(url: "https://api.music.apple.com/v1/storefronts/us"). Error = .developerTokenRequestFailed.
I have tried with one app that was previously set through Apple Developer portal and it works. As soon as I change its bundle identifier (which creates a new app identifier) it has the same problem. And there is no place to check MusicKit anymore, at least not for me.