I know this comment is directed towards something different ...
BUT ...
They start with a simple calculation of how much extra CO₂ warms the planet on its own, then check that against real‐world CO₂ and temperature records.
What is this "simple calculation" and what are the results? ... and have these results been testing under controlled laboratory conditions? ... specifically, what is the numerical relationship between CO2 concentration and irradiation ... from ppm to W/m^2 ... quite a few of us here have been looking for this information ... a link is fine ...
The IPCC has the scientific community running their computer simulations under four different scenarios, from "safely ignored" to "hellish inferno" ... and these simulations produce distribution curves, not discreet results ... however, these scenarios are based on irradiation (W/m^2), and we don't know how much CO2 is takes to change the irradiation ...
Except you said it was a "simple calculation" ... and without seeing these calculations ... or the results ... kinda makes me think your making a mistake here ... carbon dioxide doesn't have enough mass to change climate, and certainly not cause any catastrophes ... it's a "one molecule, one photon" kind of universe these days, that alone refutes CCC ...