for me, once I had reached my new baseline of no phone, suddenly I noticed the buzzing became downright annoying. I knew it wasn't anything important. I was turning on Do Not Disturb mode more often to shut it up.
I went from worrying about what I was missing to being annoyed that I was being pinged so much. Sure enough, I'd take a glance at my screen, and there was nothing I needed to care about.
My behavioral changes are much less dramatic walking around a city, of course.