However, there are factors which will happen which we don't have the ability to quantify. CO2 is the dirty word. We know that CO2 encourages plant growth. And that plant growth consumes more CO2. I look around my house and I see nearly nothing but vegetation. Our own little forty six acres has around 20,000 trees over four inches in diameter. All converting that nasty CO2. In between those trees there is grass and other vegetation all converting that CO2.
There is most likely a stabilization point at which the increased plant life processes the increased CO2. I don't see how anyone can say with straight face that they know even roughly when this takes place.
Anyone that actually knows what they're talking about is worried about Water Vapor and Methane, Carbon Dioxide is an oceanic (due to acidification) rather than an atmospheric concern regarding climate change. I suspect it's role in acid rain back in the 80s and 90s is how it became the lamen's goto but in terms of warming it's not what climatologist worry about beyond a baseline reference.
The reason Carbon Dioxide is a useful baseline is becuase it's both a potent greenhouse gas and a significant component of our atmosphere. All things being equal, more means warming and less means cooling. That being said, it was only the catalyst, the sudden spike during the Industrial Revolution kicking off the current warming trend. On it's own however it doesn't explain the current rate of warming, as you said, more Carbon Dioxide means more plants which eventually means
less Carbon Dioxide. It's self-correcting. The problem is that that initial warming caused an increase in evaporation and Water Vapor is significantly worse if you want to avoid warming. Once the Water Vapor hit a critical mass, it in turn triggered the melting of permafrost leading to the release of Methane (which is to Water Vapor what Water Vapor is to Carbon Dioxide). If Methane levels reach critical mass as well, game over. This sequence of greenhouse gas induced warming is what caused the Permian Warming which caused the Permian Mass Extinction and wiped out 95% of all life. With the current rate of warming 2K% faster and with our already reaching the point of Methane release we have NO margin for error to stop this from killing us all. It's already too late to outright stop global warming, as soon as Methane started getting out of the permfrost the feedback loop made it unstoppable but we CAN stop Methane trapped on the seafloor from escaping and reverse the acidification of the oceans if we take serious steps to combat global warming NOW.
Our grandchildren will still curse our names for the hellscape we'll be leaving them but the end of the world is still advoidable. In 20 years with no change though? As I said before, the reality of chemistry dooms us all even if we can't say exactly HOW we'll die.