Is it obligatory to repeat the Fajr prayer if a person prayed it while half-asleep due to anesthesia and does not know whether he completed its rak'ahs or not?

You must repeat the prayer that you concluded while doubting its completeness, because one's duty is not discharged except with certainty. You should not have entered into prayer until your awareness was complete, so you would know what you are saying and doing, due to the verse: "O you who have believed, do not approach prayer while you are intoxicated until you know what you are saying."