Notification sounds on IPhone 13 & Apple Watch
Can I get text notification sounds on both my Apple Watch and my iPhone 13?
iPhone 13, iOS 16
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Apple designed the way notifications work to either come to your Apple Watch or your iPhone, but not both. If you are using your iPhone and the screen is active, notifications will be delivered to your iPhone. If your iPhone screen is locked and not in use, notifications are delivered to your Apple Watch. This is by design.
See this link about this --> Notifications on your Apple Watch - Apple Support