So, in the end I did it by phone.
- direct online procedure was not possible because the buy date field in Apple systems was empty (airpods bought from amazon and not from apple)
- via support chat was not possible because that’s not how it works (you need to speak with the AppleCare department and they need to read you out loud some legal stuff about the contract)
- support chat scheduled me a call with generic apple tech support (answering from Albania)
- generic apple tech support just asked me one question about the product: “does it already have an accidental damage? yes/no”. That’s it. No way to verify. Sort of a honor system. Or they are willing to swallow the cost of people doing this within the 60 days and after an accidental damage. (probably a rounding error)
- then generic tech support proceeded to connect me to the AppleCare department (answering from Ireland). They asked me the SN (which can be read off a sealed box no problem) and the date of buy (again, based just on my word, no proof of sale from amazon needed) and inserted it in the database, so now they could activate the AC+. They read me the legally required lines about the contract, then sent me a temporary link to pay via email.
So that’s how it goes (in the EU, could be different in the States).