It looks like the move has started as 294 is going out of T3. There is a BA help desk / agent at the FL help area. I asked the AA staff if there are plans to set up a F dining area similar to T5 and they weren’t sure. The BA agent definitely didn’t understand what I was asking as she said they have moved from T5 and no longer use that lounge.
The potential F dining area — has direct access to the kitchen.
Potential first dining area.
Proof!