If you have AirPods Pro you’re eligible regardless of AppleCare or not.I have AppleCare with my AirPods Pro but, they aren’t showing on my list of devices. Also, how do you find the manufacture date?
Edited to add: I found my AC+ receipt. I bought my AirPods Pro from Apple 10.30.19. Looks like I am eligible.
All airpod pros in existence sold to customers are basically 12 months old, pretty much to the day, that’s when they came out.
All AirPod pros with this issue are eligible for replacement and will be for another full year.