Apple Music not playing purchased iTunes music on iPhone

Apple seems to be preventing me from playing music I have purchased in iTunes. In fact, the artist's music no longer appears in the store, but I have the files on my computer AND they play on my Mac. Why can't I get them to play on my phone? Will I need to burn a CD and then import the album back into my Mac? That's very 1998 of Apple.

So far, it's two artists, including two albums I purchased through Bandcamp on vinyl, but also came with downloads. They were downloaded specifically in Apple's codec, but they're unplayable on my phone.

and ever since I did this, my iTunes and my phone have been a frustrating mess. I've turned off sync library, as I don't like being backed into a corner to be able to use music I purchased - including purchases from iTunes (for this artist, an iTunes purchase has been removed/truncated in the Apple Music store, and two other albums have been deleted entirely).

I don't know if Apple's removal (or the artist's removal) of the work from the service/store has any correlation to the music not playing on my phone, but in the past year, I've spent a few hundred replacing music that I bought on iTunes and only later (after the "sync library" debacle) had the songs removed from both my library on my computer AND my phone, only to be replaced with just two or three songs on the album. I spent a couple of hours on the phone with Apple's customer service in an attempt to retrieve music I had purchased and Apple inexplicably removed - all to no avail. Even the customer service team (and it was elevated to some tech person - I don't recall who) could not fix what they'd done. To "compensate" me they gave me "10 free tracks," which aren't really free because I already paid for them and then Apple removed them... but I digress.

Short of scrapping the entire Apple brand and ecosystem, is there anything I can to do play the music I purchased?

[Edited by Moderator]