Hey there, while the new appletv models have good system-wide AirPods support, older models (of which their are millions in circulation) do not.
Other apps (Netflix, Amazon Video for example) allow you to connect to a paired bluetooth device from their playback settings menus within the app. Plex however makes you exit the app, go to settings, connect manually and then go back to the app and start the media again.
This is a lot of busywork when you are switching between devices regularly to take calls on your phone or something similar.
Would be a great feature to implement, at least for me!
Thanks for reading!