This is The Viridescent Tiara. It is licensed by Tapas.
I was a normal grad student until I woke up in a world right out of a novel I wrote as a teen. But danger’s on the horizon—the character I became was originally destined to die AND people are out to get me! Even though this character’s past was full of villainy, I’m using my insider knowledge to survive the flame of the Azure Ring, settle debts, and make things right for the House of Latia! Can I earn the trust of the hero and get ahead in this world? Are there secrets that even I don’t know?
The main character wakes up in a novel they wrote as a teen. She has a stepbrother and her mother (i.e. his stepmother) are introduced early. The brother accidentally jumped out of a tree he had climbed and landed on her. The mother wanted to punish the brother for this, but the protagonist persuades her to send him to an academy instead.
Years later, both of her parents die in a carriage accident (it was a ship accident in the original story, but she wasn't able to prevent it), leaving the position of head of the family ambiguous. She isn't related to the family by blood, and her brother is too young. To temporarily secure the position until her brother comes of age, she puts on a magical ring that will burn anyone not of the family, unless they know the spirit's true name.
Found by searching mangaupdates for the tags Author Transmigrated to Own Creation and Stepsiblings
