Why is she still there?

So the Duke adopted her, so she’s not going to die just because the OG daughter is there. She’s not leaving because Euclis was originally her only way “out” but he betrayed her so she’s looking for another way out (another character with a higher interest) before the story actually starts and leads her to her end.

Also she isn’t instantly leaving because she’s technically powerless compared to these other characters and escaping would mean they’d find her quickly. She’s also not originally from that world so it’d be harder for her to live as a commoner. That’s why she has to depend on the characters.