FWIW, I just helped a friend with her 2012 MacBook Air...it still had MacOS 10.8 Mountain Lion installed and as a result it was having issues with browsing and email as today's requirements for same were not being met by the installed software suites.
When I checked for updates, it came back as "NO UPDATES AVAILABLE"! It seems there was no path to update beyond 10.8.5 without at least one intermediate upgrade to 10.9....
Long story short (I know, too late!) - It was ultimately updated all the way to Catalina 10.15.7.....and the Software Update alert was still nagging to upgrade to Big Sur, even though the hardware wouldn't support it.
