Looking for a Book Where the Thirteenth Prince Takes the Heroine for His Sworn Sister, and She Secretly Sends Messages for the Fourth Prince While Under House Arrest

At first, the idea of becoming sworn relatives was just a joke, and nobody took it seriously. But when the heroine sneaked through a hole in the wall during the Thirteenth Prince's confinement, she later carried messages between the Fourth and Thirteenth Princes and entered the Fourth Prince's harem. I think it was a System quick-transmigration story.