An error occurred while upgrading to Big Sur

Sorry but the profile is showing " MacBook Pro 16″, macOS 10.15 " and that is Catalina but you are taking about and update of Big Sur 11.xx.

What version of Big Sur is installed Now?? What update of Big Sur is being attempted ?? By what method is the update being used. ??

If this update is for Big Sur 11.5.2 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. Also Software on the computer interfering with the download process including Anti Virus Software, 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 11.5.2 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 11.5.2 version and once downloaded run the installer from the Applications folder.

2 - Restart 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 Method # 3 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.

What was the Error Message saying - exactly