Use PS4 controller's bluetooth "Wake-Up" signal as trigger?

I figure it should be possible, but have no idea how much effort it would take, I’m afraid it’s far more involved than I can handle. But who knows?

As long as my PS4 is powered, I can wake it using any of my controllers. However, my PS4 and TV are connected to a smart switch, so I first have to power them by closing the switch (using HA). Since the controllers use Bluetooth, is it possible for HA to intercept this Wake-Up signal and be triggered by it as well?

I still have a CC2540 lying around, would that do me any good? Any pointers in the right direction (or towards people who have already done this :wink:) are welcome!