I’ve had the same thing happen since updating to Watch OS 9.4 and iOS 16.4(.1).
NowPlaying no longer activates on the Watch when audio is playing on my iPhone. I can manually start Now Playing on the watch but it defaults to trying to connect to audio on the Watch. (I never play audio directly from the watch). I have to navigate up one level and scroll down to the iPhone connection. About 1/3 of the time, I get an AirPlay error message that it cannot connect to the phone. If you retry it connection it usually connects then.
However a few minutes later, the Now Playing app is auto closed and you have to go through the whole process again. That removes the benefit of using the Watch as a remote control for the phone audio. I regularly use my Watch that way while moving around the house or in the yard while not keeping my phone in my hand or pocket.
This was working until recently but now it is just broken.