That's because before she thought she was the duke's actual daughter, even if illegitimate. The moment she gained her other life's memories and knowledge from the novel the situation became entirely different, because to her knowledge she would be executed the moment it's revealed she is not the duke's daughter. She is now living not among the family but among potential executioners. Of course she would want to run away.
If she had thought deeper about it there’s other options than bringing that much attention to herself. Ik I said she could say she wants to go on vacation after her engagement is broken, but she could’ve even said that as soon as she regained her memories. If she wanted to get away that badly, she could’ve easily said she’s leaving and go no contact, or just simply run away to another country. Correct me if I’m wrong, (I haven’t read this in a bit) but no one really cared about her whereabouts and she almost never talked to her fiancé. It’s likely no one would’ve hardcore searched for her.
She can't leave because she's the fiance of the crown prince. Even if she barely talks with him, she is still expected to attend social events as his partner to confirm their alliance, so the duke wouldn't allow her to suddenly leave somewhere. And in numerous manhwas going rogue for a noble is easier said than done, especially when magic can be used. She would just be brought back. Besides, as she states in the beginning, she has no money of her own, and her standing in the duke's house is shaky. Servants basically mock her behind her back, and she lives in the annex, not the main house. And her "family" doesn't really like her either, until she suddenly tries to do something for herself.
So she tries to tackle those problems: break off the engagement so she can actually leave and earn enough money so she can leave the family and live independently (since her actual father is in a coma and can't help). She is not very succesful initially, but it's not like she is stated to be a genius. She is just a normal girl with a bit of otherworldly knowledge.
While I still disagree with the idea that they’ll bring her back, let’s say that’s 100% the only thing that would happen. She still didn’t have to go out of her way to break it off. She really could’ve just stayed no-contact with him and gathered money in secret, but when she outwardly acts different from the og girl it’s obvious people are gonna take interest in her. What I’m trying to say is that if she really wanted to she could’ve, but for the sake of the story she didn’t.
I’ve only read chapter one, but why wouldn’t she just live quietly until the girl gets adopted? Her engagement would be naturally ended as it’ll go on to the other girl, and she could just say she wants to go on vacation to a villa somewhere far away since she wouldn’t need to do anything anymore. They always make it such a complicated process for something that can easily be solved, though I guess that makes more content for the story. So repetitive though.