I can’t speak from experience, only observation.
GW put out a game called Inquisitor which was the closest thing to a 40K RPG they published directly. It was a 56mm game. It’s been a long time since it has been supported, but it has lived on in the community under the heading Inq28 (using 28mm). https://www.reddit.com/r/Inq28/comments/182y7xi/where_are_the_rules_for_the_inq28_game/ is probably a decent place to start looking for rulesets, and https://28-mag.com/ has a lot of adjacent content.
In GW’s current rulesets, Necromunda is probably their most narrativey campaign game. https://start-warhammer.com/necromunda/
If you want an actual RPG then C7 publishes two games. Imperium Maledictum and Wrath & Glory.
Amber Diceless which compares stats with GM fiet based on the situation.
Everway which also compares stats but if things are close has the GM interpret a picture card.
DramaSystem which is designed for PvP play and trades tokens for conceding a scene (and multiple tokens can be spent to force another player to conced).
Fiasco which does use dice, but not (as random number generators) to determine outcomes. A player, on their turn, can choose to establish a scene or hand that responsibility off to the rest of the group. Whoever doesn’t do that picks if the outcome of the scene is good or bad for that player’s character (subject to the availability of good or bad tokens in the pool). Second editor ditches the dice entirely and adds cards instead, I haven’t played that version.
For the Queen isn’t a traditional RPG. It provides a card deck that asks questions about characters. Figuring out the answers lets everyone learn about all the characters (including their own).