By not even speaking, he lays out exactly how many fucks he has to give for Hayden's Utopia Justifies the Means attitude at the cost of every life he has trampled over to achieve it. Although the Doom Slayer cooperates with him because their interests are temporarily aligned, he is not happy about how many people Hayden's actions have gotten killed, and he really does care about stopping Hell's incursion into this plane of existence.
You even see the Slayer hesitate from pressing the self-destruct button when he sees the "VEGA Backup" button. He quickly presses the backup option and takes the chip now holding VEGA, as if hoping no one would notice his Out-of-Character Moment. It might be because VEGA actually helped him, instead of trying to control him like Hayden did, and the Doom Slayer is returning the favor.
Furthermore, if the Slayer is in fact the original traitor of Argent D'Nur from the background lore, he might be showing a bit of his heroic atoner side to ensure VEGA—whom he sees as an innocent in all of this—doesn't die because of somebody else's actions just as his people died from his own.
One of the collectable dolls of the game is of Doomguy himself. What does he do when he picks it up? Give the doll a fistbump.◊
Upon the Doom Slayer reclaiming the Crucible, there's a brief moment of peace when several spirits of his people—more specifically the Night Sentinels—show up to admire him. The one in the center even salutes him. They show up later in the ruins of Argent D'Nur, guiding the Slayer as he frees the Wraiths, and stand watch as he goes to confront Olivia Pierce/The Spider Mastermind. If it's true that the Doom Slayer IS the traitor that sold out Argent D'Nur then the Night Sentinels might be saying they finally forgive him for his betrayal so long ago and are helping him to end Hell's grasp on Argent D'Nur forever.