How can I import a digital copy of a new album into Music and sync it with my iPhone?

When Apple first launched the iTunes Store in 2003, the songs had DRM.

The record companies let Amazon start selling non-DRMed MP3s in late 2007 – hoping to set up a competitor to the iTunes Store that would keep Apple from having too much leverage over them. I believe that at that time, the iTunes Store had demonstrated that people would pay for electronic music if you made buying it convenient. The store also had a flat price for songs purchased individually, and the record labels were eager to change that.

There was a deal that let the record companies set several price levels for songs, in return for Apple getting the right to sell non-DRMed songs. Apple started selling DRM-free songs some time in 2009.

You can tell the DRMed ones because they have a bit rate of 128 Kbps and a type of "Protected AAC". The non-DRMed ones have a bit rate of 256 Kbps and a type of "AAC" or "Purchased AAC."

if the music is DRM-feee, you can add it to the Music library on your Mac by using the File / Import menu item.

Note that offline listening copies of Apple Music subscription songs will have DRM on them, so that if you stop subscribing, those copies will stop working.