As I wrote a few weeks ago, 16.2 broke the ability to AirPlay to speakers while plugged into an external monitor on iPadOS. If you’re still on 16.2 then you can get around this by using a Shortcut to set the audio output destination to an AirPlay device.
One caveat, I’ve seen reports that if you upgrade to 16.3 the audio doesn’t play. It selects the source, but no sound comes out.
Guess I’ll be staying on 16.2 for now because it’s the least broken version of iPadOS.