There's no misunderstanding that extends the romance plot. It's a character moment for fl about overcoming a feeling of helplessness/uselessness. She found out that everyone already knew her secret and she feels like she hasn't accomplished anything. She'll overcome it by helping somebody out later.
It feels obvious that someone tried to poison the Duke, but they switched foods. He has reasons not to trust people he just met and she has reasons to hate him. This could be solved by simple communication. I predict she'll start falling for him and THEN she'll discover how she actually died. Also her plan is pretty selfish when she could just quit.
I fear the FL is just a bit too oblivious or blinded by revenge to think about the whole picture. I noticed it throughout the more recent chapters but she wasn't aware of what goes on in the dukedom as much as she had originally thought. She also isn't good at connecting the dots, though that might have also be due to her consistently working











The demons, the partners, the emotion. AAAAAAAAAA