Well, frankly, there’s no way to prove the existence of genetic bottlenecks, or to put same into a geographical or temporal context. It’s not a bit unlike the guy who claimed that everyone currently alive is descended from a single individual who lived in southern China in 1500 BC — information invented by a computer model.
I should say, *if* there were large numbers of death assemblages *dating* from the the supposed super-eruption (and I’m not one to think there every has been such a thing, Toba or anywhere else) found in various places on Earth, and the associated genetic samples (which would obviously have to survive in sufficient shape to be sequenced) from each of these places could be studied and classified, it would probably show that the dead have the same genetic material as moderns, give or take tens of thousands of years of random mutations.