Apple support does not recognize AirPod serial numbers

I am certain that I have the correct serial number for my AirPod set, derived from my iPhone settings' AirPod info per Apple instructions.

I wish to replace one lost airpod, but Apple's replacement screen, chat, and phone support all reject the serial number. I can't even schedule a store visit, because Apple requires a valid serial number to do anything.

I bought the set directly from Apple. I did replace one airpod previously; does Apple limit users to one replacement? If not, how do I get Apple to recognize the serial number?