Big Sur 11.5.1 update failure

Check in Applications folder for Application called Install Big Sur - if one exists there, Drag and Drop to Trash and Empty Trash.

Are there any AntiVirus, Disk Cleaner, Optimizers, Defrag, VPNs 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. Any of the above will also interfere with the download process

There are several ways to download the Big Sur 11.5.1 update. 

1 - Connect to Router via Ethernet connection and restart the computer in Safe Mode and then open the Apple Apps Store and get the Full Installer of Big Sur. It will be the 11.5.1 version and once downloaded run the installer from the Applications folder.

2 - Resart the computer in Recovery Mode ( INTEL Command + r ) and choose Reinstall macOS. It too will download the full Installer and commence the installation. For M1 CPU the Recovery Mode is Here

3 - This method may seem unnecessary but sometimes the Router Restart clears Network issues from ISP to Apple Servers

Shutdown Router. Shutdown computer and disconnect all External Drives. Restart Router. Connect to Router via Ethernet Cable. If via Wifi - Disconnect all other Devices using the Wifi - want the Maximum Bandwidth only for this computer. Restart computer in  Safe Mode. It does a Repair Disk, Clear System Cache files and only load Apple Software, extensions and Fonts. Will load slowly - Normal. Once Logged in - open Apple Apps Store and  Get the Full Version of Big Sur. It will take some time and several pauses will occur - normal. Countdown clock may say 15 minutes but in Real time may be 30 minutes. Same goes for clock at 10 minutes could be 20 minutes in Real time. Eventually , Full Installer will download and a New Application in Applications Folder will present called Install Big Sur. Stop there and perform a Time Machine Backup. If desired - have an External Drive - Copy & Paste the Install Big Sur Application to external drive for future usage - making a Bootable Installer. Now run the Installer.

Have found this method more reliable than the Software Update which is very iffy at best

So, just for the record, It did download and install ?

Suggestion, for the future, try not to let the OS get so behind on updates. Early version of a new OS usually has bugs that are fixed in later versions. Letting the OS stay at 11.1 and moving all the way to 11.5.1 newest is not suggested.

Good so it worked and resolve you original issue.

As for Software Updates and all the settings enabling Auto this and that. It should have or may have notified there were updates but were overlooked or missed ?