hello,

   please follow these step for notification for new mail

    On your computer, open Gmail.
   In the top right, click Settings Settings and then See all settings.
   Scroll down to the "Desktop notifications" section.
   Select New mail notifications on, Important mail notifications on.
   At the bottom of the page, click Save Changes.

If you use inbox categories and turned on notifications for new mail, you'll only get notifications about messages in your Primary category. If you turned on notifications for important mail, you'll get notifications for everything marked as important.

I've done that several times. It makes no difference.

I've tried to tell Windows 10 (in the notifications and actions setting) that it should accept Firefox as an app which can create notifications.

Again to no avail.