Mars indeed would be the only place left to go, at least as far as any organized society is concerned, should the super volcano blow it’s top.
This isn’t something anyone can “prep” for, with skies around the globe literally darkened for years by volcanic ash, no crops are going to grow anywhere, not to mention global temperatures plummeting us into a form of a natural nuclear winter. Again for years.
It’s an “ELE” (extinction level event), like was said in the movie Deep Impact.
So like death itself, this is pretty much not worth worrying about, because nothing can be done to avoid it or its impacts.
Web search for "Olympus Mons" (LOL!)
Sure, no one has seen that one erupt, either, but it did, too.
Sometimes, better the devil ya know...
As long as humanity isn't stupid enough to sacrifice its capabilities on the altar of controlling the weather, we possess the ingenuity to survive as a species. We are far more capable than our distant ancestors, provided we learn enough tech to do so and have the will to implement it.
Some rudimentary structures could protect access to water wells, power sources, and keep roofs from collapsing--even create new structures within the ash layers. Sufficient food for the time it takes to start converting the new mineral soil into a decent agricultural base, and recovery could be fairly fast (less than a decade). Preservation of records of the location of assets which did get buried would permit faster recovery (fuel supplies, construction equipment, oil wells, coal mines, power plants, food warehouses, etc.).
Yes, there would be a 'bottleneck' while many succumbed, but the species could survive.
As cold as this may sound, those with the ingenuity and ability and drive to survive got through the last bottleneck event, (with location and luck being factors as well), with probably far less technology to support their initial efforts. While the parasite class would be severely thinned, the survivors would be of hearty and intelligent stock if the preserved close to modern technology, otherwise, it is back to scrounging and chipping flint and sitting by the fire, listening to the elders tell tales of the wonders of long ago...in the days before the sky went dark.