What is the significance of Farquhar's heightened attention to detail?

I think the answer to this question depends on the reader. On one hand, I think his vivid and heightened attention to detail helps sell the idea to the reader that Farquhar's escape is actually happening. People often say that in the midst of some harrowing experience, like a car accident, everything slows down and they notice the oddest details. Anecdotally, I can confirm this. I remember the most odd and vivid details from a car crash that I had earlier in my life.
On the other hand, Farquhar's heightened attention to detail might clue certain readers into the fact that Farquhar isn't experiencing anything. He is imagining it all in vivid detail. This should also resonate with readers, because many people are likely to be able to claim that they have had a dream that seemed so real they weren't sure it was a dream. Scientifically speaking, there is hardly any difference in brain activity between actually seeing something and imagining it. The same brain centers are triggered in both cases. The significance of Farquhar's heightened awareness is that it makes the story believable and suspicious sounding at the same time.
https://www.nytimes.com/1993/08/31/science/seeing-and-imagining-clues-to-the-workings-of-the-mind-s-eye.html

Readers are often shocked by the conclusion of Bierce’s story when they realize that Peyton Farquhar’s escape and journey home existed only in his mind. The abrupt conclusion jolts them, just as Farquhar’s body is jolted when the rope plays out, ending his free fall. The truth of what occurred at Owl Creek Bridge is confronted quite suddenly, even though Bierce provides plenty of clues to the illusory nature of Farquhar’s experience after he falls between the railroad ties.
Many specific details in Part III of the story describe that which simply could not have happened. After fighting his way to the surface of Owl Creek, Farquhar could not have observed the veins on each leaf of the individual trees by the stream. He could not have seen “the very insects upon them: the locusts, the brilliant-bodied flies, the gray spiders stretching their webs from twig to twig,” nor could he have seen the “prismatic colors in all the dewdrops upon a million blades of grass.” Also beyond the realm of possibility is Farquhar’s hearing, in the midst of the fast-moving creek, the “audible music” of gnats humming and dragonflies beating their wings or the sound of “the strokes of the water-spiders’ legs.” His head above water, he very well could have heard rifle shots and seen the Union troops at the bridge, but in the distance, the soldiers’ forms would not have appeared “gigantic,” and he could not have seen “the eye of the man on the bridge gazing into his own through the sights of the rifle.” The rifleman’s eye is gray, Farquhar notes, another specific detail that indicates the illusory nature of his escape.
Numerous other details of Farquhar’s escape defy belief, especially toward the end of Part III as he makes his way home through a landscape both foreign and peculiar. The road he follows is “as wide and straight as a city street” but seems untraveled, and it takes him through a land with no signs of human habitation. The trees are black and form “a straight wall on both sides, terminating on the horizon in a point, like a diagram in a lesson in perspective.” That his experience is surreal is emphasized when he sees “great golden stars” shining overhead, “looking unfamiliar and grouped in strange constellations.” Reading Part III carefully makes it obvious that Farquhar’s escape is a fantasy.
Why, then, are readers so often shocked when they arrive at the final sentence in the narrative? Perhaps they respond to the conclusion of the story for reasons that have nothing to do with literary analysis. Many readers sympathize with Farquhar as he faces death. They identify with his love for his family and understand his desperate desire to go home. While reading Part III, they simply want Peyton Farquhar to survive. Consequently, many readers fail to consider, or choose to ignore, the evidence that his escape is not real. Thus the sight of Farquhar, his neck broken, swinging “gently from side to side beneath the timbers of the Owl Creek Bridge” shocks and disturbs, ending very abruptly what readers hoped for him, despite the impossibility of his escape.