Presumed. Although, if I may indulge in my own headcanon, I think Vader TOLD the emperor she was dead so that he would not be forced to continue to pursue her, whether out of wanting to continue to avoid his past self or out of a tiny part of him not really wanting to kill her.
I imagine that he would not lie to the Emperor while truly knowing otherwise. He's jamming with the dark side too much to plainly protect her like that, to know she's alive and choosing not to pursue so that she would survive. That's a very conscious choice to make and I don't think he would. He is fully dedicated to the dark side.
I think Vader has a disconnect between his conscious thoughts and his subconscious feelings. In the OT he talked and walked all big and bad, he really
believed he truly was big and bad. It wasn't until Luke dragged that shit out from deep deep down that he finally realized the truth. I dont think Vader was outright lying when he said there was "no conflict." I think he was really
trying to believe it. He's not lying to others, he's lying to himself.
More likely he's just a little too willing to assume Ahsoka's death because it's easier to deal with emotionally. Somewhere in the back of his head he knows she might have survived, but he doesn't have to face that possibility if he convinces himself she's dead. On a conscious level he's decided to ignore that nagging voice and assume she's dead. On a subconscious level, leaving her death unverified like that may provide him relief because of the possibility of survival. Deep down it secretly pleases him. That's not what he tells himself, though.
Basically same theory as you except instead of lying to others, I think Vader lies to himself. I think he does it constantly. It's part of his character. His decisions are actually driven by emotion but he validates them
after the fact with logic, like a lot of people do without realizing it.