Actually No. Apple has not offered a Standalone Update for Big Sur.
Suggestion - Shutdown Router. Shutdown MBA. Move MBA as close the Router as possible and connect via Ethernet cable. If not doable - Restart Router - Restart MBA is Safe Mode - Shift - immediately - load slowly because it does a Repair Disk, clears cache Files and Only loads Apple Software. Disconnect ALL Other devices using the Wifi - want the Max Bandwidth for the MBA One logged in - try again.
If that fails - reboot to Recovery Mode - Command + r - connect to Wifi with manually input Wifi Password - choose Reinstall macOS. This will download the Full Installer and attempt to install