Can an adult or even a baby be given anesthesia for a bris milah, or do we say that the person needs to be awake for the mitzvah?
If you are speaking of general anesthesia, R Moshe Chaim Friedman answers here for babies
General anesthesia, which is putting the baby to sleep for the b’ris, is simply not done, because virtually all practitioners would agree that it is not worth taking the greater risk of general anesthesia for such a simple procedure.
For adults and children above 13, R Avraham Kadoch (who runs WorldBrit, performed hundreds of adult brit milot and wrote a book in French on the topic) writes that they perform these brit milot under local anesthesia for three reasons
the risk of a general anesthesia makes it prohibited to endanger oneself without reason
SA OC 60:4 writes that mitzvot require intention (kavana)
anyone over 13 needs to recite himself the blessings on the mila and would lose this merit
Exceptions are people who would not agree to a brit unless under general anesthesia.
Nishmat Avraham (vol 2, pp. 189-190), for older children and adults, lists poskim who forbid local anesthesia (Imrei Yosher), who permit local but forbid general anesthesia (Sridei Eish, Shevet Halevi) and who permit general anesthesia (Maharsham, Yabia Omer). R Shlomo Zalman Auerbach and R Eliashiv also permitted.
Local anesthesia for babies is also generally permitted and many mohalim report using it (e.g., here and here) but this is not universal (R Avraham Kadoch writes against it and so does this Chabad article).