I don’t think it’s likely to lead to human extinction even if unfettered, but like ice ages and the fabled meteor, we will probably have a bottleneck event where most people, if not most species, will die.

Currently we’re only on track for something like 2-3 billion people dying, and most of the danger comes from the migrations and unrest, which isn’t really a threat to humanity as species, just society as we know it.