I've got an M1 iMac running Ventura 13.2 and my Music App has refused to play through Airplay for the past two weeks. I had this issue while running Big Sur, but quitting coreaudiod fixed the issue 98% of the time. Now, none of the fixes proposed above work.I'm still holding out hope that AirPlay on my M1 iMac will eventually work as consistently as it always has on my Intel MBP. It's improved a lot, but not there yet.
What's even more weird (to me) is that my iMac will connect and play things through the system Airplay but when trying it in Music, it doesn't work at all. It went from annoying to flat out aggravating.