I have the same problem with an Airpod 2nd Generation (not Pro). I did similar tests as you did. I didn't have this problem with my previous Airpod 1st gen. The specification page doesn't indicate for how long the battery will keep the battery level while not using it. It seems to be a common problem, for example, AirPods Battery Drain? How to Fix. Today I visited the Apple store. They did several tests and it seems my Airpods don't have any issues. They updated the firmware and I turned off the find device option. I will test it again, to see how it works. The technical at the Apple store and even over the phone could not explain this behavior. I don't use it often, maybe once per week, so I found this issue. After charging the case and the AirPods both at 100%, when I try to use it again after several days, the case is at 5%, and sometimes the airpods are not even at 100%. They only refers to the following information Apple provides:
AirPods
- Up to 5 hours of listening time with a single charge
AirPods with Lightning Charging Case
- More than 24 hours of listening time
so you can deduce the case can charge the Airpods 24/5=4.8 times, but it doesn't indicate it needs to happens with no waiting time between one charge and another, so after 3-5 days the battery is drained, without even using the airpords.
From the user's perspective, this is not what we expect, it is like having a car in your garage for a week and then the battery is drained without using the car. This is not acceptable.