MacOS 12.0 how do I get this update on my Mac desktop?

Check the Apple () menu > About This Mac panel. Look in the parenthesis of the product description line. What did you see on that panel? Late-2015 or newer? Late 2013? The latter is done with Catalina.

If Late-2014 or newer, and in System Preferences > Software Update, is a newer operating system than Catalina being offered there?

Intel iMacs from Late 2015 -> 2020 can install Monterey 12.7.5 (12.7.6 eminent). From 2017 -> 2020 can install Ventura 13.6.7 (13.6.8 eminent), and 2019 and 2020 Intel iMacs can install the current macOS Sonoma 14.5 (14.6 eminent).

You may need to use a newer browser than your current Safari. Two that should work without having to upgrade the system are Brave and Firefox.