Just reread chapter 1, and I have to wonder, why would the emperor demand that he imprison his daughter, when he knows that whatever hold he has over his daughter is what keeps him loyal? I can maybe understand the prince bluffing when he said he was going to torture her, as a way to get the guards out of the way and save her, but the whole set up makes no sense. If the emperor goes ahead and tries her as a traitor and executes her, he guarantees that the duke will rebel. If he keeps her indefinitely in prison, with no punishment but no definition on the trial, he gains the enmity of everyone and guarantees a rebellion. Then, he could send her to prison and then find her innocent and release her, maybe as a way to remind the duke that he can punish her whenever, but then there would be no need for the prince to save her. We know the emperor doesn't care about his children, so he wouldn't react impulsively just because one was poisoned. I'm more inclined to believe he poisoned the princess and framed the MC to instigate some kind of reaction from the duke. But whatever the scenario is, someone is acting nonsensically. Which is why the end result is the dead MC, even though that was what no one wanted.
And again, if the duke intended to save her, why give her a sword at all? He can't be so dumb to not understand the implications of that, and there's no way for her to effectively use a sword on anyone other than herself since she never trained with one. And as a trained swordsman himself, he should know exactly how useless giving her a sword for protection would be.
Still, I wish we could see the continuation of the story on the original timeline, just so we can see the fallout of everyone acting so idiotically.