As others have experienced I am able to "pair" and "connect" a ps4 Dual Shock 4 controller to an Apple TV (14.6) but have it immediately disconnect.
I've tested the controller with an iPhone and it pairs, connects and works as expected.
I've done all the usual - re-paired, reset controller. rebooted ATV, reset ATV. Nothing helps.
On tvOS when I pair the controller it shows the notification saying it is connected and for a second I can use the controller to navigate the menu. Then it stops working and the notification comes up saying it has disconnected. Interestingly I can use the "Identify" menu option to get the controller to vibrate - but none of the buttons do anything.
As @icpapple said it seems to be something to do with the remote taking over. And their steps work for me too.
However I've found another work around. When you want to use the controller:
First make sure your controller is paired AND connected.
Go to the "Remotes and Devices" settings screen (actually you can do this anywhere but this screen shows what is happening).
Take your Apple Remote and disconnect it from the Apple TV…
Hold down Volume Down (minus) and Home (TV Screen) buttons at the same time. A few seconds and the remote will disconnect. A few seconds later a "Remote disconnected" notification shows.
Use your controller. Yeah!
Reconnect your remote with any remote button press. Takes a few seconds. Controller will no longer work.
Sadly you need to re-pair the controller after a reboot or sleep.
That works for me!
Hope Apple fixes this as it's still a PITA.