Paid for expanded storage, yet storage remains the same

Expanding upon stedman1’s comments...

Regrettably, you are always going to struggle with an iPad that has so little internal storage. The 32/64GB devices are primarily intended for use in Educational settings, or in environments where the ability to store local data on the device is not required.

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.

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 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. 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/xc/product/MK0W2ZM

Magic? Not quite... but facilitated by the iCloud storage.

Given your storage restraints, your iPad was able to create sufficient storage space by temporarily "offloading" (effectively deleting some Apps while preserving the associated App data) - then download, decompress, verify and install the software update using the vacated iPad storage.

Having successfully installed the update, temporary files required to install the update were then deleted from the iPad. Previously offloaded Apps were then reinstalled from the App Store.

Renting cloud storage does not alter the available space on your device. The device was manufactured with 32 GB, that can never be changed.