increase store size on an iPad air 2?

Depending upon your iPad model, iPadOS can require up to 9GB storage for the OS alone.

It is impossible to increase the amount of RAM or internal storage in your iPad - as this is fixed during manufacture; what you have is fixed for the life of your device. You can, however, subscribe to a higher tier of iCloud storage - but this is not a substitute for internal storage.

If your internal storage is full, your only option is to better manage the storage that you have - and delete unused Apps or unneeded data. 

These support pages should prove to be helpful:

About storage on your device and in iCloud – Apple Support

What's the difference between device storage and iCloud storage? – Apple Support

Manage your iCloud storage – Apple Support

How to check the storage on your iPhone, iPad and iPod touch – Apple Support

Clear Other storage on your iPhone or iPad - Apple Support

“Offloading” Apps can be a helpful method of creating temporary space for a software update.

https://9to5mac.com/2020/01/21/how-to-offload-apps-in-ios-to-save-space-without-deleting-their-data/

Additional information about creating sufficient space for installation of a software update can be found here:

If you need more space for an update on your iPhone, iPad, or iPod touch - Apple Support

No. Storage size is fixed and cannot be changed after purchase iOS devices like iPads or iPhones.

iOS 15.2 should use around 5 to 7GB once installed not 15.

There may be some residual installation files or other non deleted items taking up the space.

See here to try to reduce it: https://osxdaily.com/2018/07/02/reduce-ios-system-storage-iphone-ipad/