Hi, can I just add to this thread that I get this issue as well. I get emails on the watch, but no vibration or opening of the email.
This doesn't happen if I connect my Gmail account to Outlook - then notifications come through.
I have reset/checked settings and all. It has never worked even after a firmware update.
Do appreciate your efforts! You'd think they'd do better considering the price of their products!
For anyone interested, there's someone on the Galaxy subreddit of Reddit that has developed an app that works around this issue. I've not tested it myself, but is getting good response.