TL;DR
Ignore the naysayers who claim it has nothing to do with the iTunes music store—they are wrong. Look up the album in iTunes and set the album title for your local files to the exact same title, with junk like “(Remaster)” and so on included. Then clear the artwork and download it again. Afterwards, you can rename the album back to what you want. If this doesn't work, then it will never work for that album, so stop wasting your time.
The Long Story
I still use Apple Music, the former iTunes, to manage an offline music library. I have never bought into the streaming game. It sucks for many reasons that I won't explain here. What also sucks, is how Apple Music handles album art, especially for music that has been ripped from CDs or obtained from somewhere else than the iTunes store. Very often, the album art is plain wrong. It will generally be from the correct artist, but older albums will often get the cover art of a very recent release, or a stupid compilation. I don't care about compilations, I want to know what album a song originally came from.
The cover art matching algorithm has always been bad, from the earlier days of iTunes to the latest Music app release in Mac OS Sonoma. The way in which it makes mistakes has changed over the years, but it has never made any sense. I would like to have a chat with the person who implemented it. I wonder how their mind works—if it works at all. Anyone with some vague sense of logic and a bit of programming experience can come up with a better algorithm than the current one.
And please don't tell me to add my own cover art by pasting it into the info window. Ever since it was first introduced in ID3 tags, I have hated this concept of copy-pasting the same JPEG or PNG file into the metadata tags of every single track of an album. What if I have an album with 50 tracks? Do I really need to duplicate the same image 50 times? That is conceptually idiotic. Album art should be stored once and then linked to the relevant tracks. It does not belong inside the music files themselves. This is one upside from how the artwork download system in iTunes/Music handles it, because it does exactly that: download a single file and then link it to each track. Now if only it would download the correct file…
Anyhow, I'll stop my rant and cut straight to the chase. How can one fix missing or incorrectly matched artwork even when you know the album is in the iTunes music store? After some experiments, I have found a way to fix some of the blatantly wrong album covers. For instance, practically all my Dire Straits albums got the same cover of some recent Mark Knopfler compilation with a red Stratocaster on a blue background. When using the “Show in iTunes Store” option on songs from those albums, it will indeed always send me to that compilation album in iTunes. However, the actual correct albums are also in the store. However, they will often be remasters, or “bonus track editions.” The title of the album in the store is for instance “Communiqué (Remastered),” while in my collection it is simply called “Communiqué” (because I care as much about what particular remaster a track came from as I care about compilations—I don't give a 💩.)
Therefore, despite many people claiming that the cover art matching has nothing to do with the iTunes store, I decided to clear the wrong artwork, rename the album to “Communiqué (Remastered),” and try to download the cover art again. And behold, it works. (Of course afterwards I restored the original album name.) The same worked for Neko Case - “Fox Confessor Brings the Flood,” which I had to rename to the silly “Fox Confessor Brings the Flood (Bonus Track Edition)” because that is the version which is available in the iTunes store.
The bad news is that this does not always work. For the Belgian band dEUS, it is totally hopeless. The matching algorithm gets stuck on linking all albums to Following Sea. I have no clue why. Again, I'd like to see the implementation of this “algorithm”—I really could use a good laugh. How can it be so bad? How can it break on stuff between brackets? Anyone who takes a quick glance at album naming should know that if something doesn't match exactly, but it does match when omitting stuff between brackets, it is likely a good match. And what about just giving the user the option to pick the correct match from multiple options if there is ambiguity? Oh no, that is totally un-Apple of course, because everything needs to be dumb and simple. Apple expects all their users to be dumb and simple.
It is rather obvious that Apple doesn't care about the ever shrinking niche of users who want to manage their own music library. This fares against their streaming income model. I even suspect this is why they subtly break functionality in the Music app, or refuse to fix bugs, like the failure to update the last played status in many cases, or the hiccups that make the whole Mac OS choke every 7 seconds when playing music on older Intel machines—see my older blog post about this.
Anyhow, if you are as masochistic as me and want to stick to the Music app to manage an offline music collection, now you have at least some chance to fix some of your broken artwork. However, it is likely I will not only ditch the Music app for something else, but the whole Apple ecosystem in the near future, because I have figured out that I have switched to open source alternatives for pretty much everything lately. Ironically, iTunes/Music was one of the few remaining things that I liked and kept me on the platform, but since they are now also enshittifying this, it leaves me with no real reason to stick with MacOS…