Fantasy Manga about a mercenary/hunter going back in time and finds out that she’s a princess

Question

I’m looking for the name of a manga that has the female lead as a mercenary or hunter(?).

She has 2 brothers(?), and a father who is an Emperor. One brother has a fiancée that died and he’s extremely heartbroken, but hides it through humor, and he’s seen as very lazy. The other brother is studious.

The way that they check if the female lead is really the princess is by using an orb to check her mana.

I think the father and brothers have white hair. At some point she had to cut her hair short and later receives a wig that looks exactly like her own hair.

It’s not "My three Tyrant Brothers"

Answer 1

This is likely How Did I Become the Princess?, aka Starting From Today, I'm a Princess?!, also identified here.

Once upon a time, ​​I was a weary, nameless warrior with neither family nor money. Some might say this was just my lot in life, but not me. When I am given the chance to return to the past, I take it, hoping to return to simpler times. However, after turning back time, I am shocked to learn that I am actually Princess Nanael, the long lost daughter of the emperor of Ovyulia. With my new name and new home, I’m dead-set on not losing my family ever again.

The main character is a warrior that recently fought and won against the demon lord, and is subsequently poisoned by nobles that feared she'd betray them. She contacts a dragon she met earlier and it grants her wish of turning back time. Upon re-awakening she discovers she's the emperor's daughter.

The emperor proves that she is his daughter by a magic ball; he and she have the same "type" of reaction to the ball, demonstrating that they're related.

She also has two brothers (twins). All 3 have white hair.

I can't confirm any of the details regarding the wig or the brother's fiance. These appear to be later in the story and I didn't find them while skimming.