MacBook Pro not syncing purchased songs to iPod Nano

my MacBook Pro won’t sync purchased songs onto my iPod Nano 5 (or any of my other old devices). I have Apple Music, but decided to purchase some of my favorite songs with the spare money on my iTunes account. I clicked to show info on the purchased songs, and it clearly says “purchased”. But it doesn’t show up on my iPod when I sync. Similar experience when trying to add a few CDs to my library for the iPod, though I had previously added these albums through Apple Music. What is going on???