That is not directly what causes the warming. In simplified terms, we have excess of greenhouse gases, we keep more heat of what we receive from the sun than what we lose, and that is one of the forces behind global warming, hitting the 1.5ºC and so on. And CO2 remains in the atmosphere for 100-200 years after emitted.
So, this "peak", if achieved, means that we are still accelerating the problem. after we peak, we will keep adding roughly as much carbon as we did in previous years (that will keep be adding to the excess). We are not sensibly lowering the amount of extra greenhouse gases, we will still be growing what is up there for the foreseeable future. And as the planet warmed up, several feedback loops have been triggered that are adding their own quota of even more greenhouse gases, like permafrost thawing. And the extra fossil carbon that we kept adding to the system all this time will now keep circulating in the new carbon cycle, is not like after 200 years it will just vanish.
This is not "things are getting better", but at best "we will keep worsening things, but not so fast, maybe in a future"