Because this involved travel from, to, or within the U.S., the U.S. DOT has jurisdiction. Although it did not involve refunds for seat fees, the DOT recently fined BA for failing to make timely refunds for cancelled flights:

https://www.transportation.gov/briti...order-2023-6-3

("British Airways PLC - Order 2023-6-3")

I suggest filing an Air Consumer complaint with the DOT; DOT will forward it to someone at BA who has the authority to make this right. More info on the complaint process here:

https://secure.dot.gov/air-travel-complaint

("Air Travel Service Complaint or Comment Form")