Old Mac Update.
Any inline way to update 2013 Mac Air to some newer MacOS than Big Sur ?
MacBook Air 13″, macOS 11.7
For a MacBook Air (13-inch, Mid 2013), Big Sur is the end of the line.
Big Sur is not one of the "most recent three" and is not supported by vendors like Microsoft and Adobe. However, it is recent enough to run current versions of Firefox, LibreOffice, the GNU Image Manipulation Program (GMP), and the commercial Affinity V2 programs (Photo, Designer, Publisher).