How can I back up my MacBook Air?

The model year of a MacBook Air is available at Apple menu > About This Mac.

An early 2014 MacBook Air can be upgraded to the latest version of Big Sur macOS 11 but no later.

See instructions in: How to download and install macOS - Apple Support  

Be aware that if you upgrade to Catalina 10.15 or later you will also need to update any non-Apple 32-bit apps. See: https://www.stclairsoft.com/Go64/

or

 https://www.macworld.com/article/232735/how-to-check-if-mac-software-is-32-or-64-bit.html

See the following Apple Support article for information on backing up a Mac: Use Time Machine to back up - Apple Support

Backing up your Mac and updating its operating system are two unrelated operations. What is your problem? To back it up you can use Apple's Time Machine app and you will need an external disk dedicated exclusively to the updates. Your machine will install any available updates when you open System Settings, then click on General on the left panel. That opens a window where you can click on Software Update to download any available updates. Installing a newer version of the operating system in a different matter. That is an upgrade. You might want to click on the link below and read the information there so you can respond with more useful input.

 Writing an Effective Apple Support Communities Question - Apple Community