Unfortunately, no, you don't get the big picture.

A habitable zone is, simply, a region of the earth that can be inhabited by humans. It's not too hot to sustain human life, nor is it too cold to survive. Most of the land area of the earth is in the habitable zone; notable exceptions include a few deserts (e.g. the Sahara--too hot and dry), and Antarctica (too cold).

Humans are fantastically mobile. By about 12,000 years ago, they had inhabited every habitable zone on the planet save for a couple tiny islands. This is with ten thousand year old technology! If the climate warms, we move. Furthermore, we have crops and animals that we use in every climate--hot and arid, hot and wet, cold and arid, cold and wet, whatever. We bring what we need to where we need it.

If the climate warms by 20C (no model of exceeding any tipping point gets anywhere close to this), all the ice melts everywhere, there are mass floods, mass starvation, mass extinction...the survivors...just...move. They move to arable land inside a habitable zone.

It could be the most immense catastrophe ever to befall humanity and...yet...it's not a direct existential threat because we can move, and the climate varies widely across the globe.

After that, the Atlantic Conveyor could collapse, plunging the Earth into an ice age after the catastrophic hothouse and....guess what!...we move again to the new habitable zones.

The scale of suffering and death, and the scale of ecosystem destruction would be horrifying, almost unimaginable.

But we would survive as a species. The only way we wouldn't is if we found some other way to kill ourselves at the same time (or failed to tackle some other external threat because we were too busy trying to cope with the environment).

So no, it's not a direct existential threat.