my iwatch is paired with my phone so are my ear pods. when i leave for a run the connection drops. From reading another question im thinking its over Spotify not working on the watch without the phone

My iwatch is paired to my phone and so are the ear pods. When I leave the house and phone at home for a run Spotify doesn’t work , am I right in thinking Spotify won’t work unless the phone is near. Once they are all connected through Bluetooth and I listen to a radio app should this work once all are connected through Bluetooth. My watch was asking me to listen on phone or watch when I was trying it with Spotify. It’s a new watch , iwatch 6 and my first time having one so I’m a novice 😀