It's not airplay
*
The music app in the watch is acting as a remote for the Music app in your phone, and the phone is using bluetooth to send to your AirPods.
Apple has made decisions to give you the best battery life on the watch, and the way they currently handle this situation will do that. The watch using one of it's onboard radios to stream music from the internet, and then using bluetooth to send to your AirPods is battery intensive.
Someone the other day had similar issues, when they go for a run, they have to wait till they get a short distance away from their house and the phone and watch drop their bluetooth connection before starting their running music directly on the watch. If they didn't, it would start to play on the phone, and then drop out once they got away from their house, and they'd have to re-select and re-start their music on the watch.
If your phone is going to be close to you anyway, the way it works is probably best.
*It does say airplay, But it looks like a bug/oversight/strange decision/laziness on apple's part, and they don't differentiate between airplay (to a HomePod or other third party speaker) and bluetooth (to AirPods, speakers, or headphones). It just says "airplay" if it's playing somewhere besides the phone speakers no matter if it's via airplay or bluetooth. I have a sonos roam which supports both methods. In playing around just now, it says airplay for both , but for airplay it has a speaker (white box with 2 circles), for bluetooth has a speaker (side facing speaker cone) with a bluetooth symbol. There is a second line that says "iPhone -> roam" in airplay mode, while bluetooth just says "iPhone"
You can try Apple's feedback, or a brief and nicely worded email to Tim Cook, with an explanation of why you want to play directly on the watch, such as the person above where it complicated the start of their run. Chances are pretty slim that Tim will personally read the email, but the team that handles it are good about getting things to the right people.
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