Turn off email Sync (Only)

Yes.

In iOS, you can disable notifications in an app-specific manner in the operating system's settings.

On VAHR, go to Settings -> Bluetooth -> Smart Notifications.

There are two options: During activity and not during activity.

In both, you can turn off email notifications.

In iOS, you can disable notifications in an app-specific manner in the operating system's settings.

On the phone? That would disable all notifications for an app. You can't disable notifications to the Vivoactive HR while having it enabled for the phone for specific apps.

That would disable all notifications for an app.

Yes, it would. If the goal is to stop email notifications from getting forwarded to the watch but still receive notifications on the watch for other apps, that'll do the trick.

You can't disable notifications to the Vivoactive HR while having it enabled for the phone for specific apps.

You can, but not on an iPhone. If you want email notifications on the phone but not the watch, get an Android or Window 10 Mobile phone.