Fate's Masquerade

Full game not yet out, but demo available on Steam and itch.io.

As a child, you witnessed the fall of your noble house, leaving you with many burning questions about the tragedy. In search of answers, you arrive at the imperial palace to serve as governess to the empire's young princess.

Though you try to distance yourself from the chaos of court intrigue, when the young princess suddenly falls ill, you have no choice but to seek the help of one of the princes.

It seems that'd be one of two princes, who happen to be the game's LIs.