Unable to free up space on iPad Air 2

As described, storage fragmentation is the likely cause of failing to release usable storage. A factory restore will completely reset the iPad - but you'll first need to ensure that you have a viable iCloud or iTunes backup:

How to back up your iPhone, iPad, and iPod touch - Apple Support

When you are happy to proceed, you can perform the factory restore - at conclusion of which you can restore your backup:

Restore your iPhone, iPad, or iPod to factory settings - Apple Support

Are you certain that your were deleting the App (or Apps) and not instead "Offloading"? Offloading only removes the App itself - and not the associated App data and files.

If your iPad is not performing as expected, try a forced-restart - as this will often resolve an isolated software issue:

Force restart iPad (models with Face ID or with Touch ID in the top button)

If your iPad doesn’t have the Home button, do the following:

1. Press and quickly release the volume button nearest to the top button.
2. Press and quickly release the volume button farthest from the top button.
3. Press and hold the top button.
4. When the Apple logo appears, release the top button.

Force restart iPad (models with the Home button)

Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.

As you may be aware, it is impossible to increase the amount of 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.

Upgrade to iCloud+ - Apple Support

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 may 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

External storage options can often help with managing limited internal storage. Depending upon your iPad model, the iPad will either have a Lightning or USB-C port - and may therefore require either an Adapter or USB hub to connect the USB Storage device. If your iPad has a Lightning port, you’ll need an Apple Lightning to USB3 Camera Adapter:

• Lightning to USB 3 Camera Adapter

https://store.apple.com/uk/xc/product/MK0W2ZM/A

If you’re really having issues getting this to work, one suggestion I can make would be to backup your iPad on the computer, once it is a fresh backup, do a restore to factory and do the update. After the update you can restore your backup. This will bring everything back to the state that you had it when you did the update except it will now have the new iPadOS version. You can also try to do the update using the computer, this will use the computer storage for the update and not the iPad so it may be able to use the computer to do the update still without you having to delete anything off the iPad.

If you have it connected to the computer and you do the backup. On the same screen that pops up you can restore it from there. The other thing you can do is go to Settings > General > Transfer or Reset iPad > Erase All Content and Settings and follow the prompts that come up. Keep in mind you are going to want to backup the iPad before doing the restore as this WILL delete EVERYTHING on your iPad so if you don’t have it backed up, you will not be able to get data back.