This idea that everyone could/should just be ‘situationally aware’ anytime there is a hawk around is foolishness...
I’d think it’s largely dependent on the terrain and tree cover...where there is surrounding forest or large shade trees this idea becomes a pipe dream.
I have a pair of broad wing hawks that have been here for a several weeks, I’ve only spotted them a couple times and only know they are here when I hear them calling to one another as one or the other of them adjusts positions in the timber...
...the rest of the critters almost never react to them when they’re doing this... and generally only react after the hawks have picked off a chipmunk or something.
Being a bird watcher and someone who actively works at IDing birds by sound these days, I’m nearly constantly tuned in to the ambient bird noise when I’m outside or have the windows open, to the point that it can be a distraction...
....with that in mind, I can attest to the fact that there are a few species of hawks around here that can be in the immediate area and go undetected by the other wildlife.
There are enough trees around here that hawks can post up and wait, and/or glide through and strike before the resident birds, squirrels and chipmunks have time to react... I’ve seen it happen many times....
I’ve sat on our covered porch purposefully listening to the bird calls, seeing how many I could ID by sound, and while doing so have had a red shouldered hawk swoop in and take mourning doves before any bird sounded the alarm....she got so good at it she started to just flush them, and then arc around and hit them in the air as the took the predictable escape route.
But I’ve seen it happen the other way too, where the song birds sound the alarm ... maybe it was the wrens or the towhees that sounded the alarm first, then the blue jays come to investigate, etc. ... and then Mrs. Hawk flys off knowing she’s about to get harassed...
A few years ago I had a big fat fox squirrel and a young Cooper’s hawk in the yard for three mornings in a row... the hawk was too green to know how to take the squirrel, and the squirrel would lazily avoid his attempts, several times in a row, until the hawk would just sit and watch the squirrel feed, rather puzzled... it was all pretty amusing.
Simply put, it can happen many different ways... and what works for one person who knows it all in their small part of world does not translate to success for others... and of course old Ma Nature likes to mix it up and put young hawk against old squirrel just for giggles sometimes too.