I returned the headphones to the service. It turned out to be a fake. I bought used headphones from an unofficial reseller (in a pawn shop). I was misled by the fact that the headphones had a warranty in the apple program, a paper receipt, system animations, a software version and good hinges. I also saw a video on youtube where it was claimed that many details of the original headphones can be seen in the top cover if you shine a flashlight through it. This could all be a fake.
After that I bought airpods 3 from an official seller. Now I am satisfied. The sound is much better than the fake (not louder, but better). System sounds are also different. So the conclusion, either take a friend with you who knows how the original airpods sound, check the software version, or buy from an official seller.