Apple Music Only Playing Previews of Songs
If it's stuck in preview mode try signing out on other devices. Just worked for me... Pretty annoying if I have to upgrade to the family plan or whatever to be signed in on two devices, deal breaker.
As long as you are using the same Apple ID on all your devices you should not have to upgrade to the family plan.
As this article:
Turn on Sync Library with Apple Music - Apple Support
says:
If you subscribe to Apple Music, you can turn on Sync Library to access your music library and music that you've downloaded from Apple Music on all of your devices.