That’s not quite the case.
As before the aircraft and flight crew are provided by mainline BA.
You probably know that the British Airways Regional (BAR) operation was incorporated into BA CitiExpress (BACX), now BA Connect. The BACX crew now fly the BA connect fleet, while the BAR crew operate only the 767 on the JFK route.
So to answer you question Aircraft: Mainline, Flight Crew: Mainline, Cabin Crew: Connect.
1L.