I suspect (or, to be honest, I hope) that Pauliana "killed" the princess herself to establish the end of the Bikpa royal family as official fact - while in truth, she only knocked her out, so she could offer her a chance to start over in secret. If the princess was just going to die here, then there would have been no reason to build up her character as another noble daughter being used as a disposable tool by her family, much like Pauliana herself.
I feel like Pauliana would emphasise with her, and would want to offer her the same choice she received - to honour her name and lineage and die, or to throw those away, and live with pride as her own person in the new empire. That's the kind of "kindness" that the Emperor would appreciate, after all.
Plus, the "death" happened offscreen, Pauliana isn't holding a weapon, and the blood in the last frame is smeared on the floor, rather than pooling out from a wound. A perfect setup for a misleading false death. If the author wanted to make a point of Pauliana's pragmatic mercy, then the focus of the scene would have been on her resolve in the act, not the Emperor's reaction to it. That's probably the biggest clue, for me.
'Course, I could be wrong, and the author just drew this part a bit weird. Wouldn't be the first extremely important event to happen offscreen. But I'm holding out hope until proven otherwise.