I have a MacBook Air 13 inch, mid 2012 running macOS Sierra version 10.12.6 and I’m trying to upgrade to macOS Catalina through Software update and also the App Store. Neither show any available macOS updates. How can I update to Catalina?

Using Safari only, visit How to get old versions of macOS - Apple Support

Catalina does not support any 32-bit applications, and some applications, printer, and scanner drivers may not have been updated by their vendors to support Catalina. I recommend that you run the free Go64 application to see which products on your SIerra implementation are 32-bit.

Perform a Time Machine backup of Sierra before any upgrade, and do not reuse that Time Machine drive for Catalina backups. Use a new, separate TM drive for Catalina backups.