Sorry, I don't have a PS4.

Another solution, *maybe*, is to connect the Momentum 4 via the USB-C cable to the PS4.
According to the Sennheiser website, the USB charging cable can also be used as a wired audio connection (at least on PC(MAC)).
See the Sennheiser site on this subject.
https://cdn.sennheiser-cloud.com/help...

If the PS4 already has Bluetooth connectivity, there's no need for a BT adapter.
The BT-T100 (or another quality adapter) is only needed if the audio transmitter (stereo, TV or other) does not have BT internally.
Enjoy your listening!