While she herself does not have a much notable role, her presence in Utakata marks the point where the war reaches its most chaotic stage. And whenether or not she is rescued determines the ending of the game.
She seems to fit the general perception of japanese noblewomen of her era. Polite and demure, she understands that as the daughter of a noble family, her duty comes before her wishes and even her life.
That said, some of her actions also go against the expected behavior of a princess. She considers both Zen and Shu more as her best friends than vassals, and has complete trust in them. A piece of concept art also shows that she is not averse to manual work, like cooking.
Zen is Sakuya's treasured childhood friend, and she values him greatly. Whenether he values her the same way depends on the player actions, but if she is rescued Zen is shown to respect and care for her. Perhaps to protect her feelings, Zen keeps her ignorant of Shu's actions and his own mission.
Like Zen, Shu is Sakuya's childhood friend, and she trust him without question. Given Shu's manipulation and little care for her wellbeing it's doubtful he feels the same way. Sakuya's is ignorant of Shu's wrongdoings for the entirety of the story, and it is unknown what she would think of him if she knew.
Zaji is Sakuya's benefactor during her stay in the Asuka Village. After her rescue he allows her to stay in the village until the political climate recedes enough to return her to Sekishu without consequences. She is thankful to him for it and the two seem to have a civil relationship.
Lord Ujiyasu is Sakuya's father. The nature of their relationship is not explained besides the expected respect Sakuya has for him as her father, but the fact that she believed Shu's words that he had sent her to Kazama without telling her first hint at the possibility of a cold and distant relationship.
Kaede and Sakuya are not shown interacting directly, but taking a piece of concept art and her dialogue in the "Two Flowers" ending as evidence she seems to be aware of Kaede's existance and treats her with kindness. It's not known if she is aware of Kaede's connection to San.