Problems syncing music from Mac to iPhone

I own a mac and an iPhone. Both OSs are up-to-date. I also subscribe to iCloud, and am paying for 2 tb of storage space, something like 75% of which is currently free. I have lots of free storage on my Mac and on my iPhone as well.

I have a bunch of music on my Mac that I loaded from CDs. I've copied the files into the music library on my Mac. I can see them and use them in my Music app on my Mac. However, they are not replicating over to my iPhone, and I can't figure out why.

I would have expected that that replication would happen automatically by way of Apple's cloud. Given that that doesn't appear to be happening, however, I connected my iPhone directly to my Mac, opened the iPhone from the Mac, navigated to Music, and explicitly requested a sync of my Music. The process goes through the four steps super fast, as though there's nothing to sync and, in fact, nothing gets synced. No error message is presented.

I vaguely recall that Apple decided a few years ago that they would not accomodate in the Music app Music that was not purchased via iTunes. Is that what's going on here? Is the software tacitly saying, "Sorry, but you didn't purchase that on our store. We won't handle it."?

Any help? Thanks.