Why are my barely used Apple headphones not charging properly?

One of the drawbacks of Lithium batteries, not just the ones used in Apple devices, is that if left nearly discharged or fully depleted for an extended period of time, they lose their ability to be recharged. This may be the case here. As such, I suggest that you pay a visit to your local Apple Store or Apple Authorized Service Provider and they should be able to both verify the headphone's battery condition, as well as, replace the battery if required. FWIW, I typically recharge my seldomly used devices (that have these batteries) once every two to three weeks to make sure this doesn't happen. It was a "lessons learned" experience for me.

It shouldn't be, but you can get the Apple Technician to quote you a price before they perform any work on your headphones.

Ref: AirPods Replacement, Repair, and Service - Apple Support

Can you describe what "barely used" means? Are these the Apple AirPods Max headphones? How old are they? Do you leave them discharged for long periods of time (think months)?

You're very welcome!