So maybe I’m misreading this but based on the dialogue (with trash translations tbf) it sounds like Sanji isn’t fully aware he’s using conqueror’s haki
He’s tapped into it from the start of the chapter but can’t consciously control it (Killingham says as much)
Now I’m wondering if the end of the chapter is supposed to signify his full awakening or if he’s getting the Zoro treatment until later in the story
The way i read it that are First He was using it crudely at the begining of the chapter to Attack but at the Same time it could be also acos
Then He was using acoc coating for defense
At the end He Masters it
You are right that some of the dialogue inplies that sanji believed He only unlocked acos, a new Level of armament
However the only Problem with that is that kham verbatum States Omen can only damaged by acoc so i think even If that would be the Case He would be aware at the end
Its a difficult to translate chapter imo from the raws i have seen