Firstly need to fix the " Weak Security Warning on my Wifi " Recommended settings for Wi-Fi routers and access points This will involve logging in your Router as per instruction from the Maker of the Router or from the Internal Service Provider and change some setting to make the Wifi Signal from Router more Secure.
Once that is fixed >>>
If this update is for Big Sur 11.5.1 - the error message can be misleading. There are factors like poor Wifi connection, slow wifi connection, too many other people downloading at the same time and Apple Severs are overloaded, Software on the computer interfering with the download process, running behind a VPN and or / if via wifi too many Other devices using the wifi at the same time reducing the Bandwidth to you computer. Best Results are via Ethernet Cable to Router
There are several ways to download the Big Sur 11.5 .1update.
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 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
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.
