Spinning ball of death on update downloads

What is the output of the Terminal Command below

softwareupdate --list-full-installers

Does Big Sur 11.7.1 appear in the list ?

Terminal command below will download the Full Version and place a new application in the Applications folder called " Install Big Sur " Just launch it like any other application and follow the prompts

softwareupdate --fetch-full-installer --full-installer-version 11.7.1

Try booting up your Mac in Safe Mode, and then, try updating again.

Ref: How to use safe mode on your Mac - Apple Support

You are welcome and thank you too.

Do come back to the Apple Support Communities ( ASC )  in the future, if / or when additional questions may arise