Presumably you are using Messages in iCloud to synchronise your iPad, iPhone and Mac(?) computer. As such, deletion of one or more messages from any of these devices will be synchronised across all devices that are signed-in to iCloud with the same AppleID.
Should you choose to do so, you can disable Messages in iCloud on your iPad:
Settings > [Your Name / AppleID] > iCloud > Messages - set to OFF
Changing this setting on the iPad alone prevents synchronisation with iCloud and your other devices, but will still allow the iPad to send and receive messages as before. Your iPhone and Mac will continue to synchronise via iCloud.
If your internal storage is full, you may need to better manage the storage that you have - possibly deleting unused Apps or unneeded data.
These support pages may 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/uk/xc/product/MK0W2ZM/A