Remove macOS Big Sur "Upgrade Now" button in System Preferences
I too do not like seeing the red badges and use the following method to remove them in System Preferences and on its dock tile on the Dock.
In Terminal, run the following compound command:
defaults write com.apple.systempreferences AttentionPrefBundleIDs 0 ; killall Dock


Note however, this is not permanent and the command will need to be run again if you go back into Software Update in System Preferences, or the system automatically checks for updates.
Also, the killall Dock command will un-minimize all minimize windows, but the command needs to be executed for the red badges to not show after modifying the plist file.
I do not know of a way to permanently remove the red badges or the Upgrade Now button.