HELP! My iPad is stuck on an outdated iPadOS!

Regrettably, you may 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 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. When performing system software updates, you may temporarily require more...

A system software update requires sufficient space to be downloaded, unpacked and verified prior to installation - major version updates (such as updating from iPadOS 18.x to iPadOS 26) 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.

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 require an Adapter or USB hub to connect the USB Storage device.

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

Back up your data; just not having one runs the risk that a random event will cause the data on the iPad to be lost. Applications can be freely redownloaded from the App Store if they're still available there.

Updating it from a computer will require much less free space on the unit itself.

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IT proverb: "All storage devices fail. It is not a matter of if, but of when."

One should plan backup strategies accordingly.

Note, too, that should you forget your iPad's passcode, and enter too many incorrect ones, you will lose your data. After a certain number of tries, the iPad will go into a state where the only way to get back in is to wipe all the data stored o it. Nobody will be able to save non-backed-up and non-synchronized data then – not even Apple.

What is your backup plan for all the precious data and apps used daily?