i can't answer that directly, because i don't have a bt device connected. i wouldn't do that, because many bt devices always broadcast in the room... I would (my way) connect the hdmi to the tv, then a toslink splitter out of the tv and connect two sony headphones. then you have two independent headphones that will work without interference. the headphones are always on sale. it's worth the wait... the apple tv is a cool thing anyway. i need 2 remote controls less... have fun--- (BT headphones -
https://www.digitec.ch/de/s1/product/sony-mdr-hw700ds-wireless-surround-kopfhoerer-over-ear-kopfhoerer-headset-2485516)