This was driving me crazy. The album artwork showed up in mini player, visualizer, in the finder, get info, etc but the album artwork did NOT show up in the album, artists, or recently added cover views. I knew this would be a problem when I sync a new iPhone so I had to solve it. I won't bore you with details of my personal specs and large music collection (lots of Phish shows) or my MANY attempts to solve it (re-importing, deleting databases, clicking and un-clicking preferences, FOR DAYS). Here are my conclusions and solutions (TLDR scroll to Solution 4):
Conclusions:
1) iTunes and Music handle album artwork completely differently and for various reasons seem incompatible for direct import
2) The artwork is still imbedded in the files as JPG or PNG, but because of the way it was added to the new database it doesn't show up everywhere
3) They want you to stream and cloud everything now, but I'm not giving up my 20-year digital music collection just because they want to re-brand the software and streamline the database. Files are one thing, a working LIBRARY is another.
Solutions:
1) Create a new Library. Re-import the songs directly without trying to transfer from an old iTunes (worst option, loses playlists and play counts, might still have artwork problem)
or....
2) Delete the default Music Library database (/Music/Music Library/Music Library) and hold option while opening music to open your old iTunes database. When prompted name it and save the same as where the old one was so it becomes the default. Once you point to the new music files location, it will play the songs and remember your old playlists and play counts but will probably lose the artwork in some form
3) Drag and Drop -- I learned from MacRumors user Pablo88 that you can Drag and Drop from the Get Info in the old iTunes Artwork section to retrieve a full size JPG that is even named after the file. This way you can pick and choose, grab from the old, save somewhere, drag to the new thing in Music, Get Info, Artwork. But this sucks and takes forever, so somebody wrote a script, right?
4) Install This AppleScript from Doug's AppleScripts and donate Doug some money that he deserves more than Apple because he figured this out and solved it before they did. I take credit for digging this up and testing it. I gave him $10 for saving me a lot of effort but the donation is optional, although there is a an old fashioned pop-up "nag" if you don't donate but still use the script.
On a personal note, I don't know why they had to re-invent the wheel, the old thing worked fine. But I'm old and I guess software developers never sleep. Steve Jobs is dead. Long live Steve Jobs.