Unfortunately not, I tried that too, but the PS4 does not allow Bluetooth audio devices, so also no headphones, not even Sony's own...
But as already mentioned, just connect it to the controller via cable and enjoy the great sound :-).

correct... A premium headphone from Sony that is not even compatible with its own Playstation brand is more than shameful!

Hoi
Probably not. The PS4 supports only a handful of wireless headphones. You can quickly google a list of compatible devices. You could just connect the headphones to the controller via cable and set it for audio output. This works with all wired headphones (3.5mm jack).

The Sony 1000XM3 were not designed directly for gaming. Nevertheless, they are a great pair of headphones.