The SAN AC club was the lounge for BA flights at one time when BA's service was 747 LHR-PHX-SAN. BA subsequently found landside space and built their own "brand" Terraces lounge in that satellite building one passes through going to short term parking (and baggage claim too I think? Have not claimed luggage in the main term in over a decade) I think that Terrace Lounge opened around when BA started 777 nonstop service to SAN and I was told by an AC rep that lack of sufficient premium traffic was the reason BA eventually dropped service to SAN.
I don't think any extras were offered during BA's era of using the AC use other than perhaps crackers and cheese and maybe tea sandwiches appearing before the BA flight boarding time.
Maybe AA will add more that just seating area with BA planning to restore service and share the lounge? I am not holding my breath for a tranquility fountain or self service wine bar but showers would be a great addition.
If premium traffic is much higher on the reinstated SAN service, I could see BA investing in their own lounge as they did in DFW and MIA and then fight vehemently to redirect any AA ticketed passengers with business class/first class lounge eligibility to use the AC. They use ANY argument to keep AA flyers out of the DFW and MIA lounges as they know we prefer the great amenities of the BA lounge to the (crAAp) offering in the AC club.