And there will be some collateral dammage, but humanity has faced many more threats and challenges in the past.
Humanity found solutions to overcome hunger, war and diseases and as a consequence, population grew exponentially, just like a virus.
You said it. Even though Climate Change won't extinguish us like the most anxious fear.
It will cause droughts(Yihadi-ravaged Sahel region has been like a decade suffering droughts), rising sea levels(trading metropolis are maritime), floods(there are already 2M displaced in a Chinese province) if go to worse will cause all the war, poverty, hunger and death you talk about.
The worst of this is that I think we've peaked the amount to which we can grow and avoid the impacts. Now the times of decadence are coming, as with every civilization. Or at least the time in which we stop to grow.