Does buying a car after another man has increased its price and hesitated to buy it constitute a Muslim selling over his brother’s sale or buying over his purchase, and what should be done if that is the case?

If the reality is as stated by the questioner, then there is no harm in that; because the car owner did not sell it to the one who said "I will consult," but rather turned away from him and offered the sale to someone else. Therefore, this is not considered selling over the sale of his Muslim brother, as long as the owner did not commit himself to selling to the first person.