I thought it was widely known that when Yellowstone finally does go up, that will be an extinction-level event. Most of the planet will become completely uninhabitable for decades.
Not true. We need to remember that there are more than 100 known caldera eruptions of the Yellowstone hotspot as it migrated from eastern Oregon to its present location over the past 16 million years. None of these eruptions, including the big eruption of 2 million years ago, are tied to known global extinction events over this time period.
Sure, if you were a plant or animal with a limited range too close to one of these supervolcano eruptions, you were out of luck, but we don't see global impact over the known lifespan of the hotspot. If it were remotely as bad as you claim, we would have seen some obvious signs of it in the fossil record, which we don't.
Further, why would the Earth's atmosphere become unbreathable? Sure, there's a lot of ash and gases released in a supervolcano eruption. But the Earth's atmosphere is much bigger than that and most of those gases, aside from carbon dioxide and other relatively insoluble gases, would wash out in rain. The remnant that remains in the stratosphere wouldn't have much effect precisely because of how little there is in the stratosphere.
Prepping for this is a joke. No power, no running water, no crops, no breathable air on the surface, for years and years. Your basement shelter won't keep you alive for a month under those conditions.
Enough lead time and you can prep for anything nature throws at you other than universe-scale problems like the heat death of the universe. Maybe even that can be managed successfully though I'm not feeling up to it.