How do I back up my iPhone XR to a iPhone 13pro with out using iCloud

You cannot backup your iPhone to another iPhone. Did you mean that you want to transfer data from your iPhone XR to your iPhone 13 Pro? If YES, then:

Transfer Data from old iPhone to new-

Do you have a backup created either on iCloud or on your computer?

Method 1 - Backup your old iPhone on your computer like this ➔ How to back up your iPhone, iPad, and iPod touch - Apple Support and then Restore your new iPhone from that backup like this ➔Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Method 2 - The Quick Start method and here is how to do that ➔  Use Quick Start to transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support

Axel F.