Hello carlgordonjenkins,
Since this involves Gmail, we would suggest reaching out to their support, as they are going to be the experts in how their notification system works.
You may want to start here: Change email notifications - Computer - Gmail Help
Be sure to check the notification settings for Safari:
- Click on Apple Logo in upper left corner of monitor
- Click on System Settings > Notification > Safari
- Confirm the notification settings are correct
Additional information on how to set up notifications is available here: Change Notifications settings on Mac - Apple Support
Have a good day.