Apple started to experiment with animations for playlists before they introduced it for album artwork too. Currently it's not possible to store these in the cover art archive unless you convert them to GIF which comes with a hefty quality loss.

A few examples of releases with animated cover art:

• ‎Stella & Steve by BENEEMusic
• ‎if i could make it go quiet by girl in red
• ‎folklore by Taylor Swift
• ‎JAGUAR by Victoria Monét

It's not just digital releases but also physical ones that can have audiovisual cover art.
Fear Inoculum by Tool includes a 4 inch HD screen and 2-watt speaker that plays a music video:

• https://www.youtube.com/watch?v=KCjUwqZ5lrk
• https://www.youtube.com/watch?v=QY1DquGnlCM
• https://www.youtube.com/watch?v=Ca7ZJnDgS74