Is it worth replacing the battery in the iPad Air 2 or is it too old?

Personally, I wouldn't replace the battery because the iPad Air 2 cannot be updated beyond iPadOS 15.7.8 and that will become more and more of an issue as time goes by.

If you decide to do it, it costs $119 if done by Apple in the U.S. See: iPad Repair & Service - Apple Support

You would probably be better off using the money that you would do for that to get a new iPad. It’s not going to be getting anymore updates beyond iPadOS 15.7.8 so as of now it’ll still work, but soon you’ll find apps that give errors that they need updated and when you go to update will give you issues telling you to update your OS. You won’t be able to so it’s going to be issues down the road. If you upgrade your iPad and get something newer you’ll be able to keep it updated longer and it’ll still be useful for a longer period of time.

Wrong. Mine is on 15.8.2