Hi, i would suggest please dont provide your personal details.
From what you are saying, i am now convinced that your airpods are fake. Why don’t you set up an appointment with a apple expert and show it to them, they will be able to verify it. These days, even the serial number on the box and the case is verified even for the fake ones as some companies are copying serials from the Original ones and printing the same on the whole batch.
if apple confirms they are fake take your receipt and go to the shop where you bought them for, make a noise when people are around and ask for a refund.
btw did you buy it on the 2nd of May- as shown in the check coverage provided by you. If it doesn't match the date on your invoice then something is fishy.
Also, my question to you is- WHY DIDN’T YOU BUY THE AIRPODS FROM THE APPLE STORE?
Hope this helps