Yes, it does appear like the Catalina Supplemental Update may have resolved the issue. I tentatively reopened Music with the Album Artwork folder in place, and without having rebuilt my Music Library like a few people have suggested (ie. I was using the same one that had been created by the initial Catalina install).
Music immediately showed Loading Artwork, Loading Artist Artwork (this one was new), and Updating iCloud Library. The app did grow to 17 GB after a while, but album artwork was loading up little by little in my Up Next list.
This process stopped after 10–15 minutes, and my album artwork all seems to be there. Music is sitting at 24 GB, but it’s not using up any CPU (other than playing music), and neither is AMPArtworkAgent. In fact, this latter process is now unloaded, whereas previously it would be constantly running, spiking at 100%, even when Music wasn’t showing any activity.
Fingers crossed. If you’re running Catalina and have disabled automatic updates, make sure you open Software Updates in System Preferences and install this update.