There is no single ‘extinction point’ other than becoming self-sustaining.
We will survive 3C alive and (sort of) well, just all of humanity affected, unless it triggers something like the clathrate gun - that one seems to have been mostly ruled out recently, fortunately, but there are other positive feedback loops (e.g. water vapor is a major greenhouse gas).
8C would be a major extinction event, but at that point what’s left of humanity would be fully mobilized mitigating the problem (at that point you probably couldn’t avoid geoengineering).
I don’t like the ‘temperature threshold’, ‘time limit’, etc. rhetoric - it comes mostly from politicians and it leads to ‘we can’t do anything anyway’ kind of thinking. When we’ve gone past 2C (which I’m almost certain we will), ‘we’re all going to die’ is not going to help - the problem is still there and still needs to be solved.
Note - current-ish projections aren’t that bad: but 2C is the very optimistic scenario and I’m not sure the ongoing industrial rise of India and eventually Nigeria (and other large developing countries) is well estimated there.
Thanks, I wasn’t aware of that source - though this seems - incomplete (I am aware this is probably outside of their control)
EDIT: I’m being intentionally pessimistic because I assume a lot of industrial growth - still powered by coal (at least one China’s worth) and I basically expect every target to be not met (which so far has mostly been the case).