Unable to update my iPad despite having enough free storage

It is impossible to provide a definitive answer - as the space required will vary according to your iPad model, its currently installed version of iPadOS - and your iPad's settings/configuration.

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 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 (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 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

If your iPad is capable of update to a more recent version of iOS/iPadOS than is currently installed, these support pages outline both the available methods by which the update can be performed - and troubleshooting should you experience difficulties:

Update your iPhone, iPad or iPod touch – Apple Support

If you can't update or restore your iPhone, iPad or iPod touch – Apple Support

If your iPhone, iPad or iPod touch won’t update - Apple Support

iOS update and restore errors – Apple Support

Be aware that while an iPad may be capable of update, in some circumstances you may need to use a computer to perform the update*. To do so, you will need access to either a Windows PC (with iTunes for Windows installed - or the more recent Apple Devices App) or a Mac (with iTunes or Finder - as appropriate for the installed version of MacOS). Ensure that your installed version of iTunes has been updated to the most recent version; the essential device drivers are included.

Download and use iTunes for Windows – Apple Support

Update to the latest version of iTunes – Apple Support

Update software on iPhone, iPad or iPod touch in iTunes on PC - Apple Support

Update your iPhone, iPad, or iPod touch with the Finder - Apple Support

Apple Devices App (Windows PC):

https://apps.microsoft.com/detail/9np83lwlpz9k?hl=en-ms&gl=MS

(*) If you don’t have access to a suitable computer of your own, that of a helpful friend or family member will suffice. Alternatively, the technicians at the Genius Bar of your local Apple Store or Apple Authorised Service Provider (AASP) will be delighted to assist.

Genius Bar Reservation and Apple Support Options - Apple

If you have a beta profile installed, ensure this has been removed from your iPad - as, otherwise, installation of production software updates may be inhibited. This support page provides the necessary information to remove the beta from your iPad:

How to uninstall iOS beta software - Apple Support

You should note that for your iPad to install an available update, its battery must be charged to at least 50% capacity - and/or be connected to its Power Adapter. Similarly, the iPad can only be updated over a standard WiFi connection - or be updated by a PC or Mac using iTunes or Finder - over a USB connection.

To add too… Check your photo app in the ‘recently deleted folder’ and make sure you delete those files too. These files still count against storage on the iPad and iPhone. Also check in the File Folder, recently deleted folder too. It will take 30 days for the device to permanently delete them. I’ve had to do this on occasions to free up space.