Ok, figured it out, but man, what a silly way to launch.
From Lifehacker
The first thing you’ll notice when you launch the new Music app is that the tabs for Artists, Playlists, etc are all gone. They’re all now consolidated in the “My Music” tab on the far right. Tap that to see your music library. At the top, you can toggle between your music and your playlists. Tap the “Artists” dropdown and you can sort by artists, albums, songs, genres, composers, and compilations.
There’s also one very important toggle in that Artists dropdown menu called “Music Available Offline.” For me, this toggle was set to On. If you turn that off, you’ll be able add music from Apple Music’s service to your library.
Why they didn't have that set as the reverse is mind-boggling.