In this articleAALAn American Airlines Airbus A321 taxis at San Diego International Airport as a United Airlines airplane departs on August 24, 2024 in San Diego, California.Kevin Carter | Getty Images News | Getty ImagesFORT WORTH, Texas — American Airlines started pouring customers Champagne Bollinger in its top-tier lounges and cabins this fall. But at headquarters, it's not time to celebrate — yet.American has fallen behind large rivals Delta Air Lines and United Airlines in the post-Covid luxury travel ...