I am having the same problem. Siri works fine for everything but Music. When I ask sir to play a station or artist, etc. It gives the same error messages as the folks above.
I have an iPhone XS and IOS 12.1. I've tried a hard reset, that didnt help. I did disable iCloud Music Libary and that helped some. With iCloud Music Library turned off, I can use Siri for one session. But when I try the next day, it fails until I close the Music app and restart it.
This is unacceptable to me because I use Apple Music mostly in the car and on the bike. With Siri, this is a safe solution, and the reason I picked Apple Music over Pandora and Spotify. But without the Siri integration, I may as well use Pandora or Spotify. Pulling out my phone to close and re-open apps while driving or riding isn't acceptable.
Since Apple doesn't seem to acknowledge the issue and tell they are working on it, I am stopping my Apple Music subscription.