If you’re using macOS Big Sur, you know the notification system is terrible, particularly clicking that tiny X in the corner to dismiss the persistent alerts. Swiping away the notifications with your finger would be a much better way of dealing with them, but until Apple deems us worthy of touchscreen Macs, Tyler Hall has a clever solution for getting rid of them.
The other option is to switch the notification style from alerts to banner. You can do this in the Notifications System Preferences. Only a few very special apps are allowed persistent alerts on my Mac; most of them are either banners or turned off entirely. But the one app who’s notifications you can’t control? Mac App Store. C’mon, Apple.