Shutdown the Mac completely. Hold the SHIFT key and power on and keep holding SHIFT until you reach the login screen. Login and immediately after pressing Return hold the SHIFT key again. If it's encrypted via FileVault2 you will see a second login screen. Login again and again hold SHIFT till you reach the desktop. It will take longer than normal to boot. Give it a minute after you reach the desktop and then shutdown again. Start up normally.
Then retry the update via System Preferences -> Software Update
Safe Mode runs a disk scan and cleans up many system caches that can cause bizarre problems if the caches are messed up. If it still doesn't work. How much free space do you have? People with 128GB disks have had issues having enough free space to install Big Sur or later on installing an update.