My experience is from February 2023 flying First.

Check in was ok, with separate lanes for First, Club and Economy. We were dropped at the airport early by a friend that was driving out of Atlanta after we spent the morning and lunch together.

We were there before check in opened, but cannot remember the timeframe. I cannot remember a fast track through security though, and that was particularly bad overall in ATL (we also flew AA domestic from there, and TSA security was equally bad).

As others have said the contracted Lounge BA uses is the same for all other airlines plus priority pass, and they simply dedicate a small area to the left of the entrance, which was not particularly well policed when I was there, but had sign up about being for BA only. There was not further offer for First class customers and the food and drink offers was particularly bad. We therefore decided to take the train to the terminal with the Admiral Club lounge. It is small but was half empty and also closed relatively early so we only spent perhaps 40 minutes in it. They must not have that much traffic as the lounge manager recognised us from over a week early when we flew AA. Food offer was not great, mostly snacking, but definitely better that what was on offer in the BA contracted lounge. As I said the lounge closed quite early compared to the BA evening departure, so we ended up going back to the BA lounge for another drink, and then straight to the gate. The terminal train was fantastic and easy for one to go back and forth but as noted above apparently there are some works happening at the moment that may affect the schedule.

The Amex centurion lounge was not yet there last year, but if applicable, I would not hesitate to get there instead of the other two mentioned above.