You have a fairly unrealistic view of what an apocalyptic scenario would look like. Existing technology would not go bad overnight. A lot of stuff works without electricity (a relatively recent invention in the tech tree, all things considered), and electricity isn't that difficult to get going "from scratch" to begin with. Not to even mention that a world-ending meteor is something humans can, from our lofty heights far above nature, detect and even divert before it hits Earth.
Actual hunter-gatherers would be among the first to die out in an apocalypse like that, because they're wholly dependent on the ecosystem, and would lose their only source of food when prey animals go extinct. The survivors would be developed humans in whatever area happens to both not be hit particularly hard (so in the case of global ash/dust clouds, probably somewhere near the equator where farming will still be possible) and that manages to stay relatively cohesive societally.
So on an individual level survival would be down to mostly luck, but on a species-wide level it would not be.
What I think is plausible is one of those old natural self regulation that have played out over and over in the history of the planet When one exploitative species grows over beyond available resources they starve to death until a new equilibrium is reached.
This is another one of those strangely common romanticized views of nature, but it's also incongruent with reality. By definition nothing about what humans are doing to the planet (i.e. climate change, anthropocenic extinctions, what have you) is natural, and as such the consequences aren't a natural mechanism either. Humans just practically won't be able to wipe ourselves out in the same way that e.g. island animal populations may go extinct if balance is thrown off.
We can shoot ourselves in the foot real bad, but making ourselves extinct probably just straight up isn't something we're capable of. Sure, there would absolutely be a certain kind of poetic irony in humans, in our hubris, making the planet inhospitable to modern civilization (and it's possible, too), but this common metaphor of Mother Earth's immune system working to restore a natural balance is, if you forgive my being crass, complete hippie nonsense.
For example on the metric of how much of their populace has to be farming to sustain the colony. For modern industrialized humans it's some single-digit percentage, while for ants it's probably something like 50%-80% (with the rest of the ants doing nursing).
Having the intelligence and capability to rise above nature like humans have done is precisely what makes one animal species better than others. The fact that all current humans are animals was never in dispute -- though as far as I'm concerned, being human is not contingent upon being an animal.
I presume, based on prior experience, that the fixation on humans not being better/more worthy/above other animals stems from some kind of anarchist opposition to any and all hierarchies, and so I feel like I need to clarify: being above the natural world does not absolve humans of responsibility to it nor is it a carte blanche to treat lower animals however we desire. Quite the contrary. A lion is incapable of considering the ethical implications of eating meat, so we can hardly fault it for running down a gazelle, forcing it down and then slowly killing it over several minutes before eating it. Humans are capable of that, so we can fault humans for factory farming meat.