Both previous answers are good, and much more eloquently expressed than what I can write. Still, I'm going to try my best to address, particularly in relation to your example setting (which I've enjoyed playing in for the last 20 years. Damn).
The first thing to remember about Grim Dark, is there are no "Good Guys". It's all varying shades of grey. The closest that 40k comes to Good Guys is the Tau. Or arguably the Orks. The Imperium of Man is a further down that list.
First and foremost, however, 40k is based on a game. The setting revolves around soldiers and war, and the fluff reflects this. Daily life is a struggle for most humans - the entire Imperium revolves around their war. Those not on the front line work to supply the materiel. Those on the front line often don't last as long as their weapons. It's beyond harsh. And they've had 10,000 years to become accustomed to it. It's accepted as daily life because for so many of them, it is daily life.
A lot of what you've identified depends almost entirely on the story being told, and from what perspective (and where it's being presented - is it a background novel ala Black Library, or the codex/rulebook fluff - which has always been over the top). We'll explore three different examples below, based on the main character type, and the background bit.
1 - The Super Soldier
This is the most commonly written about, purely because it normally revolves around Space Marines because, 1) they're awesome 2) they're the most iconic figure in the game.
The first thing to remember about the Astartes is that, while they are humanities greatest soldiers, they are no longer human. It's been bred out of them, surgically and psychologically. They exist solely for one thing - to kill the enemies of the Imperium. They are taken as young boys, often from "savage" tribes and death worlds, and over the course of years are slowly transformed from man into Space Marine. Their humanity is all but stripped away. They know only war, trained to fight and kill with anything and everything. Some chapters are more sympathetic to their erstwhile allies, but besides knowing no fear, they also know no compassion or sympathy. The suffering of the common man does not register to them, other than as a potential threat assessment. They are the focal point of the story, and their focal point is battle. And they usually only get called in when things have already gone to hell in a hand basket. They aren't Knights in Shining Armour, they are Avenging Angels of Death.
The Chaos ones are even worse. Everything is a means to an end, and most of them redefine Crazy.
These stories, told from their perspectives, lack any kind of emotional investment in the victims, because the protagonist have no emotional investment in the victim beyond the immediate mission parameters. It's hard for them to connect with humanity - so how do you draw that emotional response from the reader? You focus the story on them and their reactions, and what dredges of humanity they still have left. Glorious last stands, steadfast commitment. Honour and Loyalty and overwhelming defiance in the face of betrayal. You instill the humanity into the inhumane.
Rynn's World does this well. The story of how the Crimson Fists, proud descendants of Rogal Dorn and one of the second founding chapters, were all but shattered by a monstrous Ork invasion of their homeworld. How the Chapter Master and a handful of his brothers won back against overwhelming odds despite the decimation of his home and his brothers. The grief, despair and disbelief at the tragic loss of their fortress monastery and most of the Chapter, the long march through hostile territory with a band of weary battle brothers, rescuing scattered humans held captive before launching a desperate and all-out attack to regain control of the spaceport and avoid utter annihilation. Heroic and glorious.
Hellsreach is another good example. How Grimaldus, Reclusiarch of the Black Templars, struggles internally with his own feelings of unworthiness while rallying and obstinately holding together the disparate factions and shattered remains of human forces during the largest Ork invasion the world had seen in thousands of years. His burgeoning respect for not just himself, but those humans he fought beside. The sacrifice of his brothers. Their unyielding spirit, and the recognizing the same unyielding spirit in those humans around him. The destruction is, of course, in extremis. The story being based off the campaign and it being, afterall, 40k.
But both of this examples provide the link needed by the reader to engage. They cannot engage on a personal level, with shared experience, so instead you provide the ideal for them to engage with. The ideals of honour, loyalty, courage are what resonate with the reader and allow the points of light in the otherwise grim dark setting.
2 - The Common Soldier
These are the stories that focus on the great bulk of the Imperial forces - the men and women of the Imperial Guard (and sometimes Navy). The bravest men and women in the whole damned Galaxy - facing all sorts of horrors with nothing but guts and a flashlight. And dying in droves.
Gaunts Ghosts and the Imperial Guard series are, obviously, the best examples of this. They are relatable characters because they are unaltered humans. The react the way you would expect someone to act. Similar to the Space Marine novels, the focus isn't so much on the victims because, again, they're soldiers and they are usually there because things have gone horribly wrong. And on a scale that's difficult for us to relate to in our modern, comfy, non-invaded by daemons, world. But they are relatable. They feel fear and terror and love, they swear, they bleed, they fight and die. And they do it for love, for fear, for penance, for duty and for honour. They do it to protect their world, and the Imperium of Man.
But these stories, as grim dark and horrific as they are, are relatable in much a similar way as stories about WWI are relatable. Because it's that human response, particularly to a galaxy of horrors.
3 - The Semi-Non Combatant
These are an interesting subset, that usually encapsulate those that aren't on the front line all the time. Most famously Dab Abnett's Inquisitor series. This is where you get to see the dark underbelly of the Imperium, and just how grim every day life is. The flip side of it is, however, that because it's an Inquisition story, what they are dealing with is the worst of the worst. Xenos atrocities, Daemonic incursions etc.
Ciaphas Cain, the dashing Hero of the Imperium, straddles this and the above type. He's a Commissar, a political officer, but still a soldier. However, his stories are told from his perspective, and offer a great insight into what life's like (albeit a narrow, conceited but often humorous one). They deal with the peripheries of the great conflicts, and are the closest you'll come to showing the impact on victims.
Sorry about the wall of text, but I'm nearly done.
How do you avoid over-doing it? You shy away from what the codex writers (and those like Gav Thorpe who started there) do and embrace what the Black Library authors do (the likes of Abnet, McNeil, ADB etc). You tell the story from a certain perspective, and you instill the humanity into it. You make the struggle personal for the protagonist. You make them fight for something they can't bear to lose. You snatch defeat from the jaws of victory. You make it matter. And never, ever, be afraid to cut that thread short - because the reality of a grim dark galaxy is that you never know when they'll die - only that they will.
If you haven't already, I'd recommend reading the following:
Ciaphas Cain (series)
Horus Heresy (series)
Battles of the Imperial Guard (series)