The Engineer's Ascent

A modern heavy machinery expert transmigrates into a disfigured legitimate daughter. She uses engineering to break locks, builds a water pump, creates repeating crossbows and black powder, saves the Crown Prince, and routs her concubine-born sister with a flamethrower. Ultimately, she divorces her husband, exposes her sister's collusion with the enemy, and takes control of the Imperial Workshop's Tiger Tally, becoming a powerful official.