I have the same problem with my AirPods Pro Gen 2 where the case loses so much battery that it only can charge the AirPods once or at best twice.
I've also had the AirPods 2 and after 3 years of usage its battery performs far better than my new APP 2.
My AirPods Pro 2 is running the latest firmware as my iPhone has the latest iOS. I've already tried reseting, unpairing and disabling "Find my" feature, but none of those solved the problem.
AirPods Gen 2 is the best Apple product I've ever bought, while AirPods Pro gen 2 is the worse.