backup iPhone without usb

No problem. It looks like a few others have chimed in and let you know that there are available cables to do the job. A simple USB-C to Lightning cable should do and you can find them at the online Apple Store ... and, I'm sure, other sources as well.

No. You can still backup your iPhone to iCloud if you can't do so with a computer.

Ref: How to back up your iPhone, iPad, and iPod touch with iCloud - Apple Support

Actually, it is possible to back up your iPhone to your Mac using Wi-Fi, but you first have to connect the iPhone to your Mac using the regular cable to set things up and enable the iPhone to connect to the Mac over your Wi-Fi network. (You may need an adapter with the cable, depending on the type of USB port on your Mac.

Once you have set up the option to allow your iPhone to connect to your Mac using Wi-Fi, your iPhone will back up using Wi-Fi to the Mac. No cable is required after that......except......if you want to update the software on your iPhone. See the red highlighted option below.

Is the issue that your notebook's USB port is faulty, or you just don't have the appropriate cable to use?

All Macs made within the last decade (or more) have USB ports. Newer ones have USB-C ports but, Apple makes a lightning-to-USB-C cable for those computers.

A Macbook Air has a USB-C port.

If you have an iPhone 12 Pro as it says in your signature line it came with a Lightning to USB-C cable.