Bluetooth audio devices are not supported by the PS4?

I bought fake AirPods called Tws Buds. I wanted to connect it to the PS4. But where I wanted to connect them is because Bluetooth audio devices are not supported by the PS4. Is that because the AirPods are fake or do Bluetooth headsets generally not work on the PS4?

As far as I know, Bluetooth headsets / audio devices can't be connected directly to the PS4. But there are certainly ways to connect audio devices as well. Just have a look on the Internet.