That might actually be the issue I’m having too, on my Big Sur system I literally cannot get any artwork no matter what.
Music.app appears to not like artwork with non-square dimensions - when I imported from iTunes into Music, most of my artwork was ignored. I manually copied out each album cover from iTunes (what a pain) and used the
convert program from
ImageMagick to resize each jpeg to 400x400 pixels, replacing the original artwork in iTunes with the resized files. When I tried importing into Music.app again, all artwork was imported as expected. I ran the convert program on Fedora, but ImageMagick is available for macOS via
Homebrew or
MacPorts. Probably someone out there can suggest other ways of resizing on macOS.
You can also tell Music (via Settings) to download artwork, and eventually it will populate most album covers from Apple's servers. This can take quite a long time, possibly several days.
EDIT: you'll probably have to use MacPorts if you want to install ImageMagick on Mavericks, as Homebrew only supports current macOS versions. I personally prefer MacPorts anyway, for ...reasons.