Dolby Vision Airplay

Hi all,

I have a Philips Oled TV with Dolby Vision / Atmos. I have taken videos on iPhone 13 Pro in 4K 60Hz and HDR.

Playing this videos on iPhone shows bright HDR videos, playing on TV with AirPlay over Apple TV 4K (1. Gen) shows „normal“ videos, Not as bright as on iPhone und TV doesn‘t show the Dolby Vision label.

Are there any settings on iPhone/TV/Apple TV to show the bright HDR Video on TV?

(Apple TV is set to 4K Dolby Vision)

Thanks.