Ok, this is annoying me. I got the iWatch SE specifically to run and to use it in the gym with my AirPods. It's not working and I don't know why. I leave my iPhone in the car because I don't need it in the gym. I used to listen to music before but now it's not working for the past iOS updates. My watch is recently updated to 10.2.
Every time I link up my AirPods press the music app on my watch pick shuffle and press play, it doesn't play anything. A pop-up comes up and says something about this item requiring a membership. I do have a membership. This is very frustrating.
As a follow up to my rant above, I think I may have discovered something that worked for me and may work for you.
I had a bunch of greyed out songs listed in my playlists that are on my watch in the downloaded section. If I went to play them I got the "apple music membership" popup. This is/was extremely frustrating since I own this music independent of Apple. Most of it was ripped from physical CDs.
I decided to poke around the watch app on my phone. I went into the music section and saw that only one of the 5 playlists I previously had on my watch were gone. It's weird because they are listed on my watch in the downloaded section but most of the songs were greyed out.
I deleted the one playlist left and then re-added all 5 of the playlists I previously had. Then I rebooted both my phone and watch and put the watch on the charger so it would re-add the playlists back to my downloaded music. Oddly enough the amount of storage I was using for downloaded music on my watch never changed.
After being on the charger for 15 minutes I decided to take it off and all my playlists were back and the music app on my watch stopped trying to connect to my phone. It seems like one or several updates FUBAR'd my playlists and the watch didn't recognize the music as local but saw the songs clearly listed, so it tried to connect to the phone to play them but when that didnt work it told me I needed a music subscription.
Anyway, I hope deleting and putting back your playlists as downloaded music helps you.