I also have almost all notifications turned off, not just for email, but for all of those apps vying for your attention. I do have notifications enabled for my "VIP's" so that I see if immediate family members or boss are emailing me. And a glance at the screen will tell me whether it is something urgent or just a random email that I can ignore until later.

My devices (phone, computer, everything) are all set to "do not disturb" during the time I do deep work, so I don't see even those few notifications.

In my gmail inbox, I have "multiple inboxes" selected, into which I filter labels for:

1 - for action

2 - waiting for

3 - delegate

4 - filing

5 - to read/watch

So I can quickly grab everything from my inbox and either archive it and put it into one of those labels/inboxes for quick handling later.