Unable to update iPad Air 2 because I don't have enough storage space.

Be aware that an iPad Air2 is capable of update to iPadOS 15.8.2; the Air2 fundamentally does not support iPadOS16 or later.

For information, here is a list of the highest version of iOS supported by the older models of iPad (for simplicity - “generations” are shortened to a number) that are restricted in their ability to be updated:

32-bit devices (obsolete)

iPad1 - iOS 5.1.1

iPad2, iPad3 and iPad mini1 - iOS 9.3.5 (WiFi Only models), iOS 9.3.6 (WiFi & Cellular)

iPad4 - iOS 10.3.3 (WiFi Only), iOS 10.3.4 (WiFi & Cellular)

64-bit devices

iPad Air1*, iPad mini2 and iPad mini3* - iOS 12.5.7

iPad Air2, iPad mini4 - iPadOS 15.8.2

iPad5, iPad Pro (9.7"/12.9" first generation) - iPadOS 16.7.8

(*) obsolete

Newer models are all able to be updated to the current version - iPadOS 17.5.1

• iPad Pro 13" (M4)
• iPad Pro 12.9" (2nd generation and later)
• iPad Pro 11" (1st generation and later + M4)
• iPad Pro 10.5"
• iPad Air (3rd generation and later + M2)
• iPad (6th generation and later)
• iPad mini (5th generation and later)

Managing Available Storage

It is generally recommended that you maintain 4-6GB of free space at all times - as your iPad needs some temporary space to complete some tasks - such as performing system software updates.

A system software update requires sufficient space to be downloaded, unpacked and verified prior to installation - major version updates requiring considerably more space than an incremental point-update. After the update is successfully completed, temporary files are automatically deleted - returning free space.

If your internal storage is full, or is insufficient for the task that you need to perform, 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

External storage options can often help with managing limited internal storage. 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/xc/product/MK0W2ZM/A

Backing up is a good first step. You can erase the iPad and upgrade it, and then restore the backup:

Erase iPad - Apple Support

Follow those instructions carefully.