I think you're probably right, but there's an enormous gap between "things start to go really bad for everyone around us" and civilization collapse.
Remember, WW2 didn't bring civilizational collapse. In fact one could argue it even accelerated industrial development. Doesn't mean much to those who perished.
Well, if we lower the bar to "Would something like WW2 happen again?" then I'm not comfortable betting against it. After all, humanity has already managed to do that on its own without any help from the climate!
You can safely bet agains any large scale war like WW2. We no longer have the money or resources for that. We can't build hundreds of thousands of airplanes, tanks, ships, guns, etc. This doesn't include nukes. We have lots of those. But any nuke war will be very very short, over in a day, not like WW2.
Climate crisis and WW2 do not compare. Many people died in WW2, but entire animal and plant species were not wiped out.
We're killing what we eat (and what we eat is nurtured by) at a rapid speed, at scale. This will first show in bearable price increases (as it already does with coffee and cocoa) and only get worse from there, think famine (in regions where this has not happened in a lifetime).
Good luck with keeping a civilization 'stable' when people are hangry at scale.
And the worst part is: While war can be ended, un-extincting is not a solved problem at all.
Remember, WW2 didn't bring civilizational collapse. In fact one could argue it even accelerated industrial development. Doesn't mean much to those who perished.