Your Apple Watch can mirror the notification settings of your iPhone, but it can also be customized.
While App Store app notifications remain on/off affairs, some of Apple's built-in apps let you customize what gets sent to your Apple Watch. In some cases you can choose who gets to alert you. In others, what you get alerted about. It's not every app, and it's not completely granular, but it can help you prevent notification from becoming interruption.
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