Do AirPods wear out?

All electronics "wear out" over time. Whether two years is appropriate for your AirPods, may depend on how you used them or what they may have been subject (environmentally) to.

I suggest giving the following support articles a try first before replacing them:

• How to reset your AirPods and AirPods Pro - Apple Support
• If your AirPods won't connect - Apple Support
• If your left or right AirPod isn't working - Apple Support

Should none of those help, you still have a few options:

1. Try to get them serviced, or
2. Go ahead and get yourself a new pair.

Ref: AirPods Service and Repair - Apple Support

Yes, they have a rechargeable battery in them.

Rechargeable batteries have a limited life.

Sounds like it’s time for a new pair of headphones.