The Favored Noble Lady

She is the daughter of an official, a noble lady, and the love child of a talented man and a beautiful woman. However, just because of the word "table", her life was completely different by a tiny margin; He is an illegitimate son, neither his direct son nor his eldest son, and he is the product of an incompatible union between his family and his maternal family. However, just because of the word "emperor", his life was completely different but not wrong at all; She and him had different genders, different surnames, and even different destinies, but two completely different people met unexpectedly...