I would like my phone to open its screen while wearing watch while getting notifications

Where you’ll see your notifications

Notifications go to either your Apple Watch or iPhone, but not both. Learn when a notification might appear on your iPhone, instead of your Apple Watch, below.

If your iPhone is unlocked, you'll get notifications on your iPhone, instead of your Apple Watch.

If your iPhone is locked or asleep, you'll get notifications on your Apple Watch, unless your Apple Watch is locked with your passcode.

Some apps, such as the Noise app, are only on your Apple Watch. Notifications for these apps don't appear on your iPhone.

No one in this user to user forum can answer a “why” question, other than to say that Apple designed it that way. When you get a notification while wearing a watch with wrist detection enabled the notification appears on your watch instead of your phone. You can still swipe down on your phone to view the notification you have received on your watch if you don’t want to read it on your watch. I would find it rather annoying to get redundant notifications on both my wrist and on my phone.

It will show both if wrist detection is disabled, or if the phone’s screen was already on.