I have had this issue too. I downloaded and installed Catalina earlier today and noticed at once an unusual memory usage while exploring the new music app.
The Music app increasingly used memory resources while I left it crunching through the album artwork updates. I returned to the computer some 30 minutes later only to be unable to exit the screensaver. My iMac (2018) crashed and the Music app started to hog resources upon restart almost straight away. I let it build up to 31.68GB of memory and just caught it before the Mac crashed again. A quick search online led me to this and other posts regarding the issue -- it appears to be quite common.
I have followed all of the suggestions listed above:
Deleting the Artwork folder in the iTunes folder,
Music>File>Library>Get Album Artwork,
Rebooting after artwork downloaded,
Open Music in safe mode.
Forcing Music to get artwork manually did seem to have helped (or, at least, some of the above measures seems to have helped) I can tell you that the Music app is still hogging 12GB of memory, but that there is no more 'loading artwork' loop -- least not at the moment!
I have also noticed that the Music app seems to spend a very long time 'checking music library' before it actually opens -- I am not sure if this is a related matter or not. I was unable to close my Music app, though, when it had finished crunching the artwork manually. Though it operated an used 12GB of memory, I had to force quit the app and then restart the computer because it became stuck in the relaunch. I shall report back with info on whether the above worked after the second restart!