Update 28 March 2026
After updating OS and iOS to 26.4, here's a snapshot of how my Music App library looks like.......

iOS is very much the same, except there's some artwork showing that does not show on Mac, an vice versa.
Yes, done all the resets, account log-outs / login-ins, de- and re-authorizations, re-syncs, empty syncs, manually sync, delete artwork cache (by the way, a lot of artwork showed in the artwork cache folder that did not show in the Music app itself.......go figure!), network reset, reboots, consolidate library, keep media organized etc etc.
It just simply does not work.
No, I am not an Apple Music or iTunes Match subscriber.
"Get album artwork" command runs empty, also cannot "Turn on Genius" in Music.
I realize I will eventually have to go "nuclear" and create a new library, from scratch. At over 40K songs, well done & congratulations to Apple for making the joy of listening to Music so unnecessarily difficult.