Bandcamp to MacOS to iOS (again)

I'm essentially repeating this question: Bandcamp to iTunes - Apple Community . The answer given there is obsolete.

I purchased songs on Bandcamp. As the original questioner said (with one change), "I was able to get the album onto my computer's [Music] app, but it is not showing up on my phone at all. I tried syncing my libraries multiple times to no avail." There is not even an error message to point out that something that was supposed to sync, didn't. The Finder sync app just claims that it synced everything--but it didn't.

This is on a Macbook Pro running Monterrey 12.5.1 with an iPhone Xr running iOS 15.6.1.

The answer given

Bandcamp to iTunes - Apple Community

gave advice for people who are Apple Music subscribers. I am apparently not one, and don't want to be one. It also linked to a help page that is obsolete for Monterrey. So a new answer is needed.

(I also think that it's deeply problematic that I can buy music, own it, and then Apple applications will not sync it to my phone. What is that about? This should be very simple: The music is there, I said to copy it, so copy it. It's surprising that this is even an issue that one has to ask about. The behavior of the sync app is not user-friendly in this respect.)