Well your tv could still have lag. You can test it by playing games without external screen, but using your PS5 controller. Then you do the same with the TV and see if there is additional lag. It could be, I am not saying it is from the tv. And maybe additionally the PS5 controller over Bluetooth adds lag too. Especially if you are not close to the system and some other stuff in the house may interfere. And if its the controller, then either it is from the controller itself or the Steam Decks Bluetooth module is not good.

I’m just brainstorming here, never looked this up online where others did “scientific” tests.