Thank you for the additional information - as this greatly helps to establish a clear understanding of the problem.
iPadOS is designed to manage it a available local cache (i.e. System Storage), reducing its size as needed to perform other tasks. There are limits however in the iPad's ability to purge data automatically. Erasing the iPad and then restoring an iCloud/iTunes backup can provide a temporary solution - however, System Data cache will again accumulate cached data as the iPad is used.
In more detail...
iPadOS 26/27 makes significantly greater use of available system storage to cache frequently accessed data and system assets. For devices with relatively little internal storage - originally attractive to users due to their lower cost - this cache will consume a larger proportion of available storage than those that have more local storage. Of itself, using local storage for caching, should not be an issue - as iPadOS will dynamically manage and reduce the size of the cache as local storage is required for other purposes.
That said, with iPadOS 26/27 you may struggle with an iPad that has so little internal storage. The 32/64GB devices are better suited for use in Educational settings, or in environments where the ability to store local 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 needs some temporary space to complete many tasks. By example, when performing system software updates, you may temporarily require considerably more.
A system software update requires sufficient space to be downloaded, unpacked and verified prior to installation - major version update requiring considerably more space than an incremental point-update. The required space, to perform an OTA update, is typically double the stated space for the installed update; after the update is successfully completed, temporary files are automatically deleted - returning free space as the process is completed.
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
Restricted storage space can become an issue when attempting to perform a system software update. One potential workaround is to use a Mac computer or Windows PC to help with the system software update - 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.
The alternative workaround, that [temporarily] reduces System Storage, 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. If you only need to clear System Storage, just restore the backup after erasing 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