When I go there for my work, for example, I see notifications _for every repo I've ever interacted with_. I would prefer it be a bit smarter, like focus in on most important repos / notifications.

I want kind of like a priority inbox of important stuff, and then a secondary inbox of stuff to ignore...

try going to github.com/watching

there should be a list of all the repos you watch

unwatch any repo you don't want to be notified of