Any Airpods connect directly to the AppleTV. You don't need the remote, phone or an app at all.

If you're using wired headphones then a $20 Bluetooth dongle will do the same.

If you use Apple headphones it works directly without the remote

Connecting AirPods to an Apple TV is literally one-button tap

I use my AirPods with my Apple TV on the daily.

It works with any bluetooth headphones, directly.