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Both the "Do not Disturb" mode & "Focus" Mode are able to control the notifications from specific apps. When the modes are active blocking notifications, clearing away any open notifications from specific apps, and stopping any further notifications from showing up becomes possible.
In addition, the "Focus" mode will also block the offending apps from accidentally opening. When"Focus" mode is on, you won't get any notifications and won't be able to use those specific apps which are selected in its settings.