Pretty sure this is Infatuation Unwanted.
Plonked right into the world of a novel she once read, Sophie simply wishes to live out the rest of her quiet life in the background. Who could ask for a better place than the sleepy village of Pellun? And it was wonderful, peaceful... until knights came in searching for Lady Amelia. The Amelia Cedric from the most powerful noble family in the Rohatin Empire?! Wait, it can't be... I'm just an extra!
A month before the start of the manhwa, the protagonist woke up as 'Sophie,' a minor character in a novel, currently working at an inn in a sleepy village. Sophie has rose-coloured hair and a burn mark on her right leg, shaped like a butterfly.
Having read the novel, the protagonist knows that Sophie is really a noble girl named Amelia, who ran away from home five years earlier to escape her eldest brother -- Duke Bastian Cedric, the antagonist of the novel -- whom she describes as "a real psychopath."
Ever since Amelia ran away, Bastian has been sending search parties after her, throughout the empire. And unfortunately for Sophie, some of her co-workers at the inn just so happen to have noticed how perfectly she fits the description of Amelia.
One of Sophie's co-workers, Zera, promises she won't rat Sophie out even if she's offered 5000 in gold. However, the next day, a group of knights turn up at Sophie's door, and it turns out that Zera told them where she was in exchange for 6000 in gold.
Sophie is taken back to Cedric Manor in a carriage, and is greeted enthusiastically by the servants, who've apparently missed her. The protagonist doesn't possess Amelia's memories, though, and only knows what little about her was written in the novel, so she claims to have amnesia to explain why she doesn't remember these people.
Now that she's home, the protagonist thinks that Bastian will kill her. To her surprise though, he embraces her warmly; it turns out that while he has psychopathic tendencies towards others, he's extremely doting and affectionate towards her, to the point where she refers to him as having a "sister complex."
Another similarly doting brother, Leonard, turns up out of the blue, having been missing for ten years. He spent those years training in a tower called the Mage's Edifice, and has now earned the title of Archmage.