Is it considered a necessity to uncover one's face before a male anesthesiologist after entering the operating room for surgery, especially given that I was unable to wear the hijab at that time?

It is not permissible for a woman to seek medical treatment from a foreign (non-mahram) male doctor, exposing her face and other parts of her body to him, except in cases of necessity or need that are considered equivalent to necessity. What occurred unintentionally or without deliberate intent is not sinful, in accordance with the Almighty's saying: "And there is no blame upon you for that in which you have erred, but [there is blame for] what your hearts intended." One must take heed and be cautious in the future. "Necessities render the forbidden permissible" and "Need is considered equivalent to necessity" are two sound jurisprudential maxims, derived from the Almighty's saying: "But whoever is forced [by necessity], neither desiring [it] nor transgressing [its limit], there is no sin upon him."