IWatch reacts to my iPhone being too close

Start a SharePlay session by holding two iPhone devices close together. With SharePlay, you can instantly stream supported content, listen to music, play games, and more in sync with a friend by holding your iPhone close to your friend's iPhone.

Start a SharePlay session by holding two iPhone devices ...

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Please re-post with details so that someone else can help.

When you bring two iPhones head to head this is what you will experience a brief sound and vibration as shown in the GIF below. This is AirDrop.

I am not aware how Apple Watch behaves.

I think it is due to name drop settings being enabled, such that now devices held close together can share a contact. This functionality can be turned off somewhere in settings.