How do I back up an iPhone 13 without a usb?

You can do an iCloud backup over WiFi. See if this helps: How to back up your iPhone, iPad, and iPod touch - Apple Support

You can also back up your iPhone using Wi-Fi to your computer.....but....you will need to allow the phone to connect using Wi-Fi first. And....that will require that you first connect the phone to the computer using a cable.

Once you have set up the phone to back up using Wi-Fi, you will no longer need the cable.

You need either a USB-A (rectangular connector) to lightning cable or a USB-C (connector with rounded edges) to lightning cable, depending on whether your computer has a USB-A or USB-C port to connect to. The iPhone 11 came with a USB-A to lightning cable.

cbeziopcbackup wrote:

I do not want to use iCloud. I want to do this manually.

Then you need to back it up to your computer.

You need to use a USB to lightning cable or USB C to lightning cable, whichever is appropriate to connect to your computer.