I believe they meant existential in the sense of existentialism and not in the sense that it may have lead to extinction, given that they went on to relate it to one's attitude towards life (and we commonly refer to events that shake up our view on this as "existential crisis"), but even if that weren't the case I find it cavalier to dismiss this as "unbelievable hyperbole" and perhaps the reason you seem to encounter it so often is that there's more truth in it than you're willing to recognize. We don't know what the future holds or what directions the past could have taken; we don't know how bad COVID may have been if there were a different set of mutations or if war had broken out in Ukraine in January of 2020. I doubt we would have gone extinct, but to pretend it wasn't an incredibly dangerous situation is folly.
As a species that has thrived from conditions as diverse as Arctic cold, desert heat/dryness, and Himalayan elevations, I really doubt that Homo sapiens is going extinct any time soon. I don't even think nuclear war would do it, since there would be plenty of survivors, although we might regress back to subsistence farming if the survivors could not sustain our technological and transportation infrastructure.
The worst pandemic we have recorded, the Black Plague, only killed between 30 - 60% of the population. At the beginning of the Covid pandemic the death rate was about 4%, and even in Italy where the medical system collapsed it was only 15%. Plus it was known early on that the mortality rate for under 40--people who will go on to reproduce--was very low. These figures are not even close to extinction level. Even the plague wasn't close to that level. So I strongly agree that fears of extinction are "unbelievable hyperbole". Was Covid serious? Yes. Could many people have died? Yes. A serious tragedy? Could have been (although I think the bigger problem, in retrospect, was shutting down the economy/society). Possibility of extinction? Not in the cards.
Every species that has ever gone extinct has had similarly impressive credentials. In the depths of time, mountains will become plains, rocks will move like water, and the hardiest survivors will falter.
