Question about Sony PS4 Dualshock 4 Wireless Controller

Unfortunately, this does not work. There are so-called "MFI" controllers that can be purchased additionally and can thus be used in certain games. But the game must support it accordingly. What does work is the use of an iPhone as a second controller. As far as I know, this also depends on the game. The Siri remot actually works quite well, depending on the game. But it's definitely not the same as using a "decent" game controller. However, Apple has improved a few things in iOs 9.3 and prevents unintentional pressing of the touch screen, for example.

Unfortunately this does not work

Works from tvOS 13 :-)

I'll say no, because Apple usually has its own Bluetooth standard and there's no Apple-licensing on the controller packaging. But I'm happy to be proven wrong ;)