Does anyone have experience pairing and using an official Sony PlayStation 3 or 4 controller with the 4th gen Apple TV?
It is my understanding that for the iPhone, a PS 4 controller can be used on a jail-broken phone using an app called Controllers for All. I'm not aware of any other methods.
Under the assumption that the Apple TV is mostly an iOS device, and if a jailbreak for the new Apple TV is possible, then I'd expect the developer of Controllers for All to try to release a version for the Apple TV.
That said, I haven't seen any word from the developer (Ori Kadosh, @cjori) that he plans for an Apple TV release.
No, but you can buy a SteelSeries Nimbus Wireless Gaming Controller for around $50 for the Apple TV (4th generation).