I'll try to put meat on some bones... and perhaps provide a better understanding of your issue.
Regrettably, if storing data and files on your iPad, 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 or Business settings where the ability to store data on the device is not required.
It is generally recommended that you maintain at least 4-6GB of free space at all times - as your iPad always needs some temporary space to complete many tasks. When performing system software updates, you may require considerably more available storage while the update is installed.
A system software update requires sufficient space to be downloaded, unpacked and verified prior to installation - major version updates (such as updating from iPadOS 17.x to iPadOS 18) requiring considerably more space than an incremental point-update. After the update is successfully completed, temporary files associated with the update process 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. 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/A
Using a Mac computer or Windows PC can help with system software updates - as the update package is initially downloaded to the computer, unpacked and verified by the computer, prior to the computer installing the updated system software on the target device.
As is, perhaps a workable remedy is to ensure that you have either an iCloud or iTunes backup of your iPad - and then completely erase the iPad. With no user-data present, you should be able to update the iPad; once updated, you can restore your backup to the iPad.
How to back up your iPhone, iPad, and iPod touch - Apple Support
Erase all content and settings:
Settings > General > Transfer or Reset iPad > Erase All Content & Settings
After the reset, set-up the iPad with your AppleID - but do not restore the backup. Perform the system software update using whichever method works for you.
Finally, restore the backup to your iPad:
Restore all content to iPad from a backup - Apple Support
