I've been in the same boat as others, always failing on attempting US domestic bookings (that show open on AA.com). So I tried from "abroad". I VPN'ed to France, opened an anon browser (Edge in this case) and connected to the French language BA site
https://www.britishairways.com/fr-fr/home#/. I did the exact same search I had been doing multiple times, this time it worked! I was able to pay and complete the booking. Afterwards, I disconnected VPN, went back to the regular BA and same old error. So, YMMV, but perhaps something else to try! Even with no French skills, anyone who's navigated the BA site more than a few times will have no problem, all the menus and buttons are in the same places. And there's always google translate.