pretty sure its this ! https://www.mangago.me/read-manga/genius_doctor_black_belly_miss/
It's not .
The mc and the crown prince didn't meet until later. First early chapters, she was busy saving her family from going broke. She became a beast tamer and sold magic beasts, and gave the business to her relatives to manage, her grandfather was so pleased with her that he gave her a library.
She was preparing and cultivating for the entrance exam. She was the only one. To have the ability to wield all 6(?) elements, this was rare. She got into the academy and made friend's. She was good at cooking too I believe, which made her dorm mates happy. She did all this whole pretending that she was a guy.
She met the crown prince in a valley while cultivating. He doesn't appear much in the beginning of the story, only in the encounter they had in the valley.
So, I remember reading this one light novel?? That got adapted into a manhwua years ago.
I remember key details like the mc being a girl but had to pretend to be a guy or else she will be killed. It was a regression(?) Or another soul the got in her body, a god tier level cultivator in their past life.
She saved her family in the brink of ruin and there was a magical beast(?) that follows her around. She met a guy in the valley while she was training. I remember they lived together for a while in a cave. The guy was actually the crown prince and was cursed with his soul broken. Unbeknownst to them the mc had a fragment of his soul in her bracelet, I forgot how she got it.
I hope someone remembers or know this T_T