You surely can control music on iPhone from the watch. Better yet, SIRI on the watch is actually better than on iPhone when control music because she doesn't pause it when you launch her. You can just raise your wrist, tell her to skip the song, lower your wrist and be done, all while music continue to play until it is skipped. Smoother operation.
I would presume SIRI on AirPods will act the same way, that she won't pause music on the watch. And I also believe "Skip" and "Volume up/down" should be native and you don't need internet for them.