How do I purchase AppleCare for AirPods?

I suspect the issue is the AirPods need a firmware update for that to work as expected. This is especially likely if they are new.

• To update the firmware start by updating the iPhone. It will need to be running at least iOS 13.2. 

Apple Releases Firmware Update for AirPods Pro

1. Launch the Settings app on your iPhone, iPod touch, or ‌iPad‌.
2. Tap General.
3. Tap About.
4. Scroll down to ‌AirPods Pro‌ and tap it.
5. The firmware number is listed under "Firmware Version."

Applecare

https://www.apple.com/uk/support/products/headphones/

Apple put a hold on the AirPod Pro firmware update, a new set will be up to date.