@OP:
The setting you'd turned off, "Notification icon during sync and push" has nothing to do with new message notifications (and yes I did read what you wrote).
I'm guessing it's one of two things:
- Some sort of third party software thing, who knows?
It sounds like this fit bracelet comes with an app monitors notifications from other apps (to mirror them to the bracelet), and maybe this has other side effects. You can try turning this monitoring off in system settings -> accessibility -> services.
- Or you might have an account level "override" for notification settings and this is the one that gets used (instead of the app level settings).
To check, please long press the account -> Special settings.