Can I back up my phone onto my iPad Pro?

Natively supported backup methods are described here:

How to back up your iPhone, iPad, and iPod touch - Apple Support

While you cannot perform a full system backup of an iPhone directly to an iPad, or vice-versa, you will find some third-party file management Apps that can be used to backup data and files to Cloud or other storage devices - including other computers and devices.

Two Apps come readily to mind, the first of which I use myself (using the Pro version) to manage and backup photo and other files to external storage:

File Browser - Document Manager (recommended):

https://apps.apple.com/gb/app/filebrowser-document-manager/id364738545

FE File Explorer: File Manager:

https://apps.apple.com/gb/app/fe-file-explorer-file-manager/id510282524

Both of the above have the equivalent “Pro” versions. If considering either, you’d be well advised to check which version is more suitable for your needs before purchasing.

You can back it up to a computeer (Mac or PC with iTunes installed) or iCloud - but not an iPad Pro. For one thing, the iOS systems are not the same.