The macOS allows most Apps to provide some type of notification on the Desktop. Overarching control of these notifications is in the System Preferences. You can do some specific control using Do Not Disturb in the Control Center. Instead of turning on DND for all notifications on your Mac, you may want to just mute one App or process. This is easy to do in macOS Monterey.
You can set this up by clicking on the Notifications area in the upper-right corner of the menu bar on your Mac. This will drop a list of your notifications. Click on one of the processes to expand the list of notifications for that App.
This is a list of Airmail emails. If you wanted to just mute this App and leave other notifications running, you would click on that right-facing arrow in the corner of the small window. This opens that notification like so.
To mute this specific App notification, click on the ellipsis and select a time frame from the dropdown list. This will set DND for that specific App or process.
If you just want to mute one App for a while, it is easy to do in the macOS.