In case you haven't noticed: If you have downloaded a file from the cloud or have had Music provide artwork, the image data does not get written to the track's file, even though you will see artwork for a track throughout Music.
Additionally, there's no way for an AppleScript to access the artworks of these kinds of tracks.
If the files of your tracks had image metadata before updating to Catalina, then you probably don't have any artwork problems with those.
My specific issue is that files on machine A that have custom artwork I applied to them and that sync via Cloud Music Library do not have the custom artwork when I download them to machine B. Instead, they have whatever artwork Apple has assigned for the album.
I had hoped that there might be an AppleScript trick to workaround this, but as I mentioned above, AppleScript wlll error when attempting access the artwork data or raw data properties of these tracks:
tell application "Music"
set theTrack to item 1 of selection
count artworks of theTrack
--> 1 , accurately detects 1 artwork
get raw data of artwork 1 of theTrack
--> error number -1728
--> error "Music got an error: Can’t get raw data."
You can test this yourself, either with the script or by trying to copy the small artwork image displayed in the top left corner of a track's Show Info window and pasting it somewhere. It won't.
[UPDATE 10.29.19: Hey! Apple fixed many of these issues in the macOS 10.15.1 and Music v1.0.1 updates.]