Weak female lead who knows ancient magic becomes strong by rejecting her family and planned engagement

Question

The female lead is a fiancée of a prince, but the prince loves her sister. The female lead has knowledge of ancient magic or something.

She then casts aside her family, breaks the engagement and lives in a house she requested with the king.

Answer 1

This might be a hit or miss, since we are lacking some concrete information.

Could this be Her Royal Highness Seems to Be Angry?

Here is a summary of the story:

Born as the Princess of War, touted as the Greatest Mage, her name was Leticiel. She lost her family and partner to the neighboring kingdom’s invasion. In order to prevent her power from falling into enemy hands, Leticiel took her own life… or that was what was supposed to happen. Instead, she woke up to see an unfamiliar ceiling. After gathering information, Leticiel realized she had somehow transmigrated into another person living a thousand years after. To make things worse, she was a talentless lady who was shunned by her acquaintances, family, and even her fiancee. There were many issues she wanted to complain about, but when she witnessed the magecraft of the world from a thousand years after… “Magecraft Maniac” Leticiel was livid at its lameness. “The magecraft level in this world is too looooow!!!” The tale of an eccentric Royal Highness blasting open her path in life using the strongest magecraft, begins! - Novel Updates

Note: I'm quoting a fan translated version of the light novel below, since there doesn't seems to be an official english translation yet. Also the manga version seems to deviate from the light novel version? After skimming through the manga I noticed that the manga was missing some key points, that are available in the light novel version (like the engagement annulment).

Why I think it fits:

1. Female lead is engaged to a prince
2. Female lead transmigrated from the past, where she was one of the best sorcerer to live. After transmigrating to the current era her knowledge is far superior to present day magic.
3. In volume 1, chapter 1 we can read her fiance openly flirting with her sister while the female lead is present

Before Leticiel’s very eyes, Rocheford was looking at her younger sister with an enraptured gaze while Christa’s cheeks were dyed red with embarrassment. He was clearly showing animosity towards Drossel while showering Christa with affection. And on top of that, Christa didn’t seem to dislike it herself.

4. In volume 2, chapter 1 she meets the king and after some discussions she managed to arrange an annulment of her engagement with the prince and she got a residence in the suburbs of the city

[...] She had been reminded time and time again that the Duke’s household loathed her, or rather, Drossel. There would be no way in a million years that he would be against her request. (I already got the engagement annulled, if I can get out of that household, it’d be the cherry on top…)

Why I think it does NOT fit:

• There was no mention of transmigration/reincarnation
• It is not clear whether it's a manga or light novel or web novel or something else entirely
• Title implies that female lead got stronger after the annulment, but in this story she is already strong after her transmigration.