How to tell the mode (Transparency, noise cancellation or none) of airpod pro when it connects to the Apple TV?
Since the AirPods don’t have a mode until they are in your ears there’s no mode before you have them live. 

Once they are live that data isn’t exposed on AppleTV. I would recommend using the switch control on your AirPods to cycle the mode until you know what mode they are in by listening.