It is not absorption of incident short wave solar radiation by CO2 that heats the air, but rather absorption of long wave back radiation.
I’m not any kind of a physical chemist, but is it not the case (1) that CO2 absorbs long wave back radiation in only limited portions of the radiation spectrum, and (2) that the long wave absorption capacity of CO2 is rather easily saturated?
Also involved in the heating process is the efficiency of heat transfer from CO2 molecules to other components of the atmosphere.
All light absorption occurs in very narrow exact bandwidths. It is an energy state phase change from one electronic orbit to another. There is only so much light in the narrow bandwidths that match the specific energy state phase exchanges within CO2. Whether it be long wave or short wave IR.