> As far as I know there is no indication that climate change will be an extinction-level threat?

We are currently living in an era of mass extinction. It's not something that's coming, we are in it, it is measurable. 75% of wild animals, insects and trees have disappeared. That is a fact, and it is not related to climate change at all: "just" to how we humans organize the world (mostly habitat loss).

Climate change will bring famines, natural disasters, and global instability (that means wars). This is yet to come.

It is fairly likely that at this rate, we will reach 4 degrees of global warming. At 4 degrees, a large part of the Earth (around the Equator) becomes unlivable for humans (it's too humid and hot, we can't regulate our temperature by sweating, we die). Which means that billions of people will need to relocate. This is not just normal wars: think entire countries that decide to leave their territory and go somewhere else, together with their army.

I don't know what the definition of "extinction-level" means (maybe you only care about some individuals of the human species surviving), but in my book that's as bad as it gets.

Entire regions of the planet could very well become uninhabitable, which would affects hundreds of millions, potentially billions of people. Migratory flows of that size would almost certainly lead to armed conflicts. It's hard to tell how this would end, but it is certainly not going to be pretty.

I’m sure you will agree that for most people, the difference between extinction level and civilization ending is academic.

Unfortunately, it will get really grim and bad that even if literal extinction is improbably (humanity seems to have already bounced from less than 10k people) it seems to be bad enough to warrant this hyperbole.

Like, if most of the tropics reach wet-bulb temperature and more than a billion people live there - that will be grim.