I think a lot of accounts are exaggerated and/or mistake muscle contractions for consciousness. But the brain is intact and still has oxygen in it for a few seconds, so there’s no reason it should die instantaneously. The idea of a “head in a jar” or a head transplant does have some possibility to it, albeit very difficult and extremely likely to fail. But theoretically if you can reconnect the head to the relevant arteries or whatever in the few seconds before total oxygen deprivation and brain death, it could work.

It’s a contentious topic, but there have been multiple studies indicating it could be true.

The implication that severed heads may, however briefly, retain the capacity for life has been supported by a number of unusual experiments over the past century in the field of head transplantation. In 1908, Dr. Charles Guthrie performed the world’s first canine head transplant, in which he attached one dog’s head onto the throat of another dog, reconnecting arteries so that the host provided blood flow to the newly-attached head. Of note, this procedure took approximately 20 minutes, and while the transplanted head displayed some simple reflexes, it quickly deteriorated [10]. Dr. Vladimir Demikhov, one of the founders of modern thoracic surgery, repeated a similar experiment in 1954. The heads that he transplanted displayed complex behavior and survived for far longer, up to 29 days, likely because of the significantly shorter time they were without blood flow [10]. Dr. White took the field a step further in 1970 when he performed the first “cephalic exchange transplantation” in primates. Although this transplant involved cervical spine transection of the animals and thus continuous respiratory support, the two heads displayed a normal awake EEG pattern after the surgery [10]. In 2015, Dr. Ping Ren performed a similar experiment with mice, and in one notable example, was able to keep the animals alive for six months [10]. While the science-fiction trope of a "brain in a jar” is impossible for the time being, these experiments clearly demonstrate that the long-term survival of a transplanted head is quite possible. This, in addition to the 1975 [7] and 2013 [9] studies discussed above, suggests that there is no functional difference between the brain of an executed human and the brain of an intact human, for at least several seconds post-decapitation.

— https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9930870

(Emphasis mine)

If a head can be transplanted as those studies indicate, it must be alive for at least a few seconds.

The same paper gives arguments against the idea of retained consciousness (right under the section I quoted), but the studies mentioned in that section still seem to indicate about 3 seconds before unconsciousness in rats.

Like I said above, from a logical perspective it makes sense. The brain is kind of the only thing that directly matters in regards to death. Every form of death besides direct damage to the brain is ultimately the brain dying because some system required to keep it alive failed. Since the brain isn’t damaged and still has oxygen in it, it should be alive for those few seconds before the oxygen runs out. I think direct and widespread destruction of the brain is probably the only way to truly guarantee near or effectively instantaneous death.

That’s possibly why destruction of the brain makes me more uncomfortable than other forms of death, immediate cessation of the self feels wrong, like the brain should be allowed to have a couple seconds to process the fact that it’s over.

I’ve seen a (non-scientific) theory that the idea of “heaven” could actually be the brain releasing endorphins upon death to make those final moments blissful. If true (and again it’s a completely non-scientific theory with no real evidence to back it up afaik), I think everyone would deserve to experience that instead of dying immediately. It could explain some people who have near death experiences claiming to have seen heaven. But I don’t know if the short time the brain is alive is really enough for that theory to be true.