How is hibernation/aestivation different from anesthesia?
I'm going to answer the question of whether aestivation/hibernation can be activated in humans or other apes, because it's more interesting.

Mammals, as a clade, have three major subgroups. Bats, shrew-likes, rodents, and then everything else including primates. One family of the shrew-likes hibernates, some rodents(but not all) and some bats can hibernate or enter a period of extended torpor. The only kind of primate that can hibernate is the dwarf lemur, which does so in a strange way(fully asleep for 6-8 months, little regulation of body temperature). Other hibernating animals regulate their temperature but keep it low, and wake to roll over or whatever every couple of days. Plus lemurs are on the edge of the mammal cladogram, so they're just pretty weird.

Phylogenetically, it's not likely(imho, but I'm not a mammalian phylogenetics expert) a primate ancestor of humans has ever had the ability to hibernate. It seems more likely that primates lost the ability if it was a capability of mammalian ancestors and dwarf lemurs re-evolved it. It's possible atavistic remnants of such a system might still exist, but extensive hormonal and possibly surgical treatments would be required to induce it. Not to mention you can wake animals from hibernation by poking them, so it probably would be a substandard anaesthesia method.