When I have apps that need updating in OSX I get a notification on the top-right corner of my screen that does not go away until I click it (which opens the app-store). Is there a way to turn these notifications off?
In OSX Mavericks:
You can temporarily disable the notifications by scrolling down in your notifications panel and switching the "Do Not Disturb" to On. My understanding is that the duration of time that this is in effect is determined by your settings in System Preferences > Notifications > Do Not Disturb > From XXX to XXX.
OSX Monterey allows creating custom "Focus" settings in Notifications & Focus.
By creating a custom Focus using a Time Schedule, and specifying specifically which apps are allowed to send you notifications you can effectively turn off all notifications.
In my experience so far this includes OS & App Store related notifications.
This is particularly useful given that the new OSX includes random add like Notifications for Safari.