I think it was unintentionally for Scarlet to die. Just like they say her death wasn't supposed to happen. That Aisha girl (Scarlet lunatic fan) just happen to imitate her and loose the replica of Scarlet's earing which was pinned down for Scarlet to be the culprit of poisoning.
Well, it said many members of the empire's former royal family were married off after the coup, right? I THINK I'm right. It was a little difficult to keep track. So it wouldn't have seemed too out of the ordinary at the time. They didn't know at the time Faris was planning some ish. I'm thinking that during Scarlet's spatting with Cecilia, he found out exactly what was going on behind the scenes and made the decision to leave her to her fate to save the country. He might've even told her about it, like you said, and she was so proud she was like, "nah, ya'll ain't using me like that, DO YOU KNOW WHO I AM? Take my head." And maybe that's part of why she was so confident that whole time in prison and during her execution.
i think the duke told scarlet the plan before she was executed. Narratively, her amnesia around her own death could be explained away by needing a catalyst/reason to get the ball rolling in the first place, but i think that amnesia could also include the duke at least hinting that her death was for the greater good or whatever.
real question is why he’d knowingly go after and impregnate a descendant of the empire’s royal lineage unless this was all some grand chess game and scarlet was intend to be a pawn from the very beginning