I can't answer your question since I don't know what the condition of your iPad air 3 is (battery wear and if its is an OEM battery etc).
But, I have been running iPadOS 16 on mine (iPad air 3 and iPad air pro M1 cellular) since it came out and its running fine, I don't notice much difference from iPadOS 15.
There is a number of things that can affect batterytime, apps that hasn't been updated to support iOS 16 or that has bugs that drains battery along with improvements (new features) of the OS that has a negative effect on the battery.
When looking at tests it seems like iOS 16.5 improves battery on iPhone devices compared to the older iOS 16 versions, especially on older devices. Not sure it applies to iPadOS but since they are quite similar i'd say its a chance it will.
But the biggest reason to update to iPadOS 16.5 (and newer when released) it that is fixes severe security flaws.
So make yourself and your friends you care about a favor, update your device