PlayStation blog:

PS5 offers seamless integration with the Apple Music streaming service with background music and music video playback, so players can listen before, during, or after their gameplay session.

How’s it work?

PS5 users can either start the Apple Music app before hopping into a game, or during gameplay by pressing the PS button on the DualSense wireless controller to access the Control Center and select the Music Function card.

And:

From there, Apple Music subscribers can find recommendations that match the game they are currently playing, or choose from a playlist in their library or other Apple Music-curated playlists for gaming.

This is far more integration than I was expecting when I first heard about this. What about Xbox?

From Digital Music News:

You can listen to Spotify, SoundCloud, and Pandora on Xbox using an official app – but not Apple Music. However, that’s not to say you can’t enjoy the service using your Xbox Series X console. A third-party application called “AirServer” hooks into AirPlay and allows Apple Music content to be remotely cast to an Xbox device from an iPhone or iPad.

The PlayStation Apple Music integration is head and shoulders better.