In the case of ATL, the terminals are really just the check-in and baggage collection areas - the international one housing the various non-domestic carriers along with customs/border etc. for international arrivals. Flights leave from the concourses, which are all connected by the underground tunnel (I’ve not used this) - because just as in the U.K. there are no separate areas because there’s no exit passport control to deal with. If interested you can have a look at the map with the Delta app.

For the OP: when we took BA226 in 2019 the Club was a bit of a zoo. There was a cordoned off area for passengers of BA and a couple of other specified airlines - the rest being pay-to-enter and Priority Pass etc - but it wasn’t noticeably more empty. There was table service, maybe only for drinks? I would say don’t get there early, but iirc the Pre line wasn’t operating in the evening so you might not be able to cut it too fine. Can’t expect a lot more at a competitor’s fortress hub - the days of operating one's own lounge everywhere are long gone.