The JFK BA F lounge is basically for BA Gold card holders and OW emeralds: The BA F pax, and a couple of BA (non-OW standard) FF card types, are normally in the Concorde Room (About the same size as the Terraces lounges upstairs). This is a separate lounge to the left when you've got through premium pax security, although I dont think any other OW FF status levels will get you in there. Its seems to be BA only.
Maybe the Terraces F lounge does nt get maybe the attention it deserves as a result, but it does nt represent what the BA F pax experience is. Its maybe that both QF and CX have chosen not to pay BA to allow their F pax to access the Concorde Room.