software updates

See the following from Update macOS on Mac - Apple Support

If your Mac doesn't include Software Update, use the App Store to get updates. 

The following may also help:

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

A late-2010 through mid-2011 MacBook Air can be upgraded to High Sierra 10.13.6 but no later version.

A mid-2012 MacBook Air can be upgraded to Catalina 10.15.7. See: How to get old versions of macOS - Apple Support

A mid-2013 or later can be upgraded to the current version of Big Sur. See: How to upgrade to macOS Big Sur - Apple Support

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install. Make sure to use Only Safari to commence the download as Others may not work

Make a Time Machine Backup Before attempting. Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina and Big Sur Only support 64 bit and there is no workaround.

Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation