Apple's engineers are obviously never going to figure this out so I'll give you the actual problem and its solution.
Your AAC files contain MPEG-4 audio metadata which tells your playback software how they should be grouped. These tags live inside the moov.udta.meta.ilst namespace. While the Music apps on the Mac/iPhone/iPad all group by album artist + album name (aART + @ alb), which is a sensible solution, the Apple Watch developers (in their infinite wisdom) apparently decided to make their version of the app group by plID, which is a unique numeric ID that Apple uses to identify the album in the Apple Music (iTunes) store.
You know, because Apple is the only place in the world to purchase music and every album ever made is available from Apple and why would you even think about buying your music from anyone else but Apple?
Of course, this means that the Apple Watch will only correctly play files that have the plID tag. This is why the files that you buy from Apple work, but any files you download from other vendors, or from CDs you've ripped yourself, won't work.
Fortunately, there is a solution to defeat Apple's anti-competitiveness, but it will take some work on your part. You need to create a unique plID for every album in your collection, and use a tool to update your files to set that value on each of your music files. I use
a modified version of AtomicParsley (command line tool) for this so I can script the updates, because doing this with a graphical tool for thousands of files in my music collection would be ridiculous.
You run the command like this:
$ AtomicParsley yourfile.m4a --plID 123456789
You can also list all of the current tags on your file by running this command:
$ AtomicParsley yourfile.m4a -t
Every track in a particular album should have the same plID, and every album should have a different plID. Unfortunately, if you use a different plID than the one Apple uses in their store, then the "View Album" feature won't work because it doesn't know where to go to. You can get the plID by copying the large number out of the Apple Music URL, for example for this album
the plID should be 201281514.
Try this on one of your albums, then add that album to the Music app on your Mac and sync it to your iPhone, and see if your Apple watch is able to play it back.