I’m Stanning the Prince (Salty Scans Version)
The protagonist was arrested for treason because her fanfic, which she wrote as a hobby, was so popular that it reached the ears of the Imperial Family.
However, thanks to that fanfic, the image of the first prince improved, and his older sister, the princess, keeps the protagonist by her side to take advantage of it politically.
Thanks to that, the protagonist can stan to her heart's content while the prince is uncomfortable with such protagonist. They bicker back and forth but they start to get closer to each other.