Function of Apple Watch

The Apple Watch you have has a 8GB of storage built in. You can download selected playlists to the watch prior to your run. This can be done in the Watch App (Watch -> Music). Remember these playlists are synced only when your watch is connected to the charger.

I'm assuming your AirPods are already paired. If not, pairing your AirPods with iPhone automatically pairs it with the Watch. No extra work!

And you will need Bluetooth headphones paired to the Apple Watch. They can be anyone's Bluetooth headphones, as long as you can figure out how to get the darn things into "Discovery" mode so the Apple Watch will seen them as a device to pair with.

I've paired 4 different Bluetooth headphones (2 of them over 15 years old). In all but the Airpods case, the difficulty was finding the instructions so I could put them into Discovery mode. You know, hold this button for 7 seconds, while standing on your left foot, swinging a rubber chicken counter clockwise around your head, and you will be in Discover mode. On another pair the chicken has to swing clockwise, so finding those instructions is critical 🤯

If you have a cellular Watch or download a playlist in advance of your run, yes. If you choose to stream, it has to be from Apple Music or (I think) Pandora.