To use your SSD with your iPad, you will require an Apple Lightning to USB3 Camera Adapter - as this provides the necessary USB Controller/Root Hub that is otherwise missing from all iPads that feature a Lightning port:
- Lightning to USB 3 Camera Adapter
https://store.apple.com/xc/product/MK0W2ZM/A

You cannot use Thunderbolt cables with your current iPad. You will require a certified USB3 Type-A to USB-C data cable. These are available from good computer stores - and from Apple:
- mophie USB-A Cable with USB-C Connector (1 m)
https://store.apple.com/xc/product/HN892ZM/A

You should note that you must connect your iPad Power Adapter, rated at 12W or greater (i.e., 2.4A @5V) to the Lightning port of the Camera Adapter.
Some additional information can be found here:
Connect external devices or servers with Files on iPhone - Apple Support
https://www.imore.com/how-use-external-hard-drives-your-iphone-or-ipad
To be recognised by iPadOS, the attached USB storage device must be formatted to FAT32, exFAT, APFS or HFS+ with a single partition. Microsoft NTFS and other proprietary formats are not supported. Formatting and partitioning, if required, must be performed using a separate computer; iPad does not provide any facilities to format an external storage device.
You should note that FAT-based formats are perhaps most useful for portable storage - in that they are generally universal are supported by most computers; APFS will only be accessible by compatible Apple devices.
As for backing-up your iPad, natively supported iOS/iPadOS backup and restore processes are dependent upon iCloud, or connection to either Windows PC (with iTunes for Windows installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of macOS).
Native backup methods offer full system backup - consisting of data and device settings.
How to back up your iPhone, iPad, and iPod touch - Apple Support
It is possible, however, to use a third-party App to backup data (not device settings) to a variety of external storage options - including third-party Cloud services, external media devices and network storage. One App that comes readily to mind is FileBrowser Professional by Stratospherix:
https://apps.apple.com/app/filebrowser-professional/id854618029
You would be well advised to review the extensive online Manual and help files to determine suitability for your needs.
https://www.stratospherix.com/products/filebrowserprofessional/filebrowser-professional-user-guide.php