Earlier quoted context omitted.
My strategy here is to default notifications off for everything other than calls and texts. And then manually open Gmail to check mail, manually open Instagram when I feel like checking notifications, etc. It’s such a better experience when you’re opening an app because you want to, and not because a notification is baiting you.
Allowing GMail to only show a notification when an email is categorized as "important" is an acceptable compromise. (Setting up a bunch of filters to manually control the "importance" helps a lot, too.)
If it's a real emergency you'll get a voice call.