Apple Music songs cannot be copied to an iPhone

I have ample storage on my iPhone (iPhone 13, but with up-to-date software updates), and I am logged in with the same Apple ID on phone and my Mac desktop (using Sequoia system 15.4). I tried to sync my Apple Music (subscription is still current and fine) from my desktop to phone automatically, but that didn't work well for some reason. I called Support and was told it's better to do it manually, so I connected my phone to my Mac and turned automatic sync off on my phone so that I could manually select particular playlists to transfer. A bunch of songs I had from the iTunes years transferred successfully, but for songs I got through Apple Music, I kept getting error messages that "Apple Music songs cannot be copied to an iPhone." Any help?