How can I get Safari 16 onto my MacBook air?

You would need to upgrade to Big Sur, Monterey, or Ventura and install all security updates. See: Apple security updates - Apple Support

Also see: Update macOS on Mac - Apple Support

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

A mid 2013 and early 2014 MacBook Air can be upgraded to the latest version of Big Sur macOS 11 but no later. See: How to download macOS - Apple Support

An early 2015 and a 2017 MacBook Air can be upgraded to the latest version of Monterey macOS 12. See: How to download macOS - Apple Support

A 2018 or later MacBook Air can be upgraded to the current version of Ventura macOS 13. See: How to upgrade to macOS Ventura - Apple Support

Safari 16 ships with iOS 16, and is available as an update on macOS Monterey and macOS Big Sur. If it is not showing up as an available update, and your bio is correct showing Mac OS 11, then your Air is too old.