Personally I'm against using any automation (aside from spam filtering) to keep your inbox clean. If I see emails I don't want, I delete them on the spot. If I see those emails frequently enough, I unsubscribe from their feed or mark as spa, if that's not possible. Over time, unwanted emails should go down, which will convert your inbox into a to-do list of sorts (if it's there, it needs to be actioned).

My work emails are in Outlook and I automatically sort into folders (and then I use search folders to see everything new).

But one thing which I was surprised helped me enormously was setting up some simple "canned replies" using Quick Actions in Outlook (my simplest is to send a one word reply "Approved"). I think this is because it seems to avoid the need for me to mentally "context switch" so much.

Filtering is still useful even in that system for sorting mail according to its context, so that one can entirely ignore everything from the context until you're ready to work on it.

E.g. if I run a book club or something via email, and all book club mail goes to a label or folder instead of the inbox, I can wait to look at it for when I'm doing book club work, instead of seeing it all the time.

Perhaps I am too old, but in case you don't use all this gmail, sieve + dovecot provide you with any imaginable flexibility.

The issue is mainly with my work e-mail, which is gmail. I get so much uncontrolled notifications from so many different places that I despise using e-mail.