Is it a condition that the anger which negates the obligation to fulfill a vow must be such that it deprives one of their sanity?

The basic principle regarding vows (nadhr) is that they are an obligation of devotion to Allah, undertaken without being conditioned on a specific purpose or driven by animosity and anger. If the motive behind the vow is anger, then it is a vow of obstinacy and anger (nadhr lajāj wa ghaḍab), and its ruling is the same as that of an oath. This applies if the person in a state of anger is aware of what he is saying while angry; otherwise, there is nothing due from him.