https://www.mangago.me/read-manga/ashtarte/ not sure but sounds a bit like this
I don't think this the one you've looking for but maybe https://www.mangago.me/read-manga/actually_i_was_the_real_one/
Could it be? “Actually, I was the Real One” here’s the link— https://www.mangago.me/read-manga/actually_i_was_the_real_one/
Is it this one ?
https://www.mangago.me/read-manga/i_saved_you_but_i_m_not_responsible/
The hair, tower, experimentation, and earth power line up but I low key dropped it early on so idk about her hair turning black and the mercenary part . I think she’s a spy sent by the holy kingdom cause they saved her or something tho

It's the trope of the "fake daughter" is actually the real one
So from what I remember the mc was born and she had a different hair color not like her mother's who was blond and her father's that was black it was brown we find out it's because she had nature powers which the duchess had and mc just inherited but for some goddamn reason the mother just didn't say jack shit so everyone just speculated she cheated even though she DIDN'T even her husband thought so but she insisted that mc was her daughter so everyone agreed until the mother died they then imprisoned the mc in a tower where she was then experimented by mages unknown to her father and brothers, we then get to see her powers and her hair turning jet black she then escape the tower becomes a mercenary?of some kind she basically does jobs to the people who took her in and now her job is to protect the "real daughter" of the duke who mysteriously came back FULLY knowing they're being deceived I think the reason she accepted the Job was to also get kinda half revenge to what her family did to her and also see it's downfall