I've never actually researched or attempted to stop them altogether, but I know you can make a configuration profile to defer them which in turn prevents the pop up / notification

Dashboard -> Computers -> Configuration Profiles -> Restrictions -> Functionality Tab

Running this command will stop the update from showing up, as well as stop the popups

sudo softwareupdate --ignore "macOS Catalina" macOSInstallerNotification_GM

This will clear the ignore list when you want to install it.

sudo softwareupdate --reset-ignored

@nelsoni will this stop the ability to allow the user to run that update entirely? Also, in the command you have "macOS Catalina" and then "macOSInstallerNotification_GM" - is there a resource you can point me to in order to determine what those values would be for Big Sur or future major updates?

After 20 years in Windows administration, I am new to Mac administration and the lack of ability to have more granular control over updates is astonishing to me.