From
https://support.apple.com/en-us/HT205547
If your iPhone and Apple Watch Series 4 (GPS + Cellular) or Apple Watch Series 3 (GPS + Cellular) are both connected to a cellular network, your watch can do everything that it normally does, even if your iPhone isn't with you.(1)
...
(1)To receive SMS from third-party apps, MMS from third-party apps, or push notifications from third-party apps on your cellular model of Apple Watch, your paired iPhone must be powered on and connected to Wi-Fi or cellular, but it doesn't need to be nearby. You also need to be signed in to iMessage on your iPhone.
I think the basic point is that your Apple Watch needs to be able to find your iPhone via the cellular network and then you do everything on your Apple Watch that you can do if your iPhone is nearby, including stream music.
NOTE: I only know of Apple Music streaming that work. If you use some other music streaming service, you need to check with them to see if they have an Apple Watch app and if the app actually streams music on the Apple Watch or is just an interface to control the streaming on the iPhone (I think this is what Spotify does).