Like, she applies to be the ML's tutor... but the process is glossed over in a few sentences, as if it isn't that hard to apply to be the Thirteenth Prince's teacher. Regardless of whether or not the ML is currently unwanted royalty, she is just a preteen herself. (She's like what, 15?) She'd more likely be a study companion than a tutor. It later says she has a reputation for being incompetent as well. How the heck did she get hired in the first place???
Plus, she gained control over the Archduke's house? When she's an unwanted child? What does it mean that "she had power over them despite the bad relationship with her family"? Can that not be glossed over, please? How did she just fire her maids when she had been bullied by them for so long? It may seem satisfying, but it's also quite... jarring when reading it. She leaves her house without her family knowing, and then it casually mentions that she's rich. From what?? Where did this money come from?
Can I get background info instead of the info dump telling me she's beautiful, beguiling, wealthy and powerful??? It also mentions she has charm, and can make people want her/like her... she spent 400 years as a sword, I'm not sure where this skill is coming from.
She also has infinite mana and can see fairies?
I'm not exactly getting her revenge plan... she wants revenge on the royal family.... but then uses a member of the royal family to do so? If you tame him and control him, how does that translate to ruining the royal family and kingdom?