With CO2 the release is instantaneous.
Instantaneous? What is your definition of that word? There are many things that happen quickly but in a relative way. To What are you comparing the release of energy from a molecule of excited CO2?
A photon takes a very short time to traverse the atmosphere and escape to space. 100 kilometres of atmosphere divided by the speed of light. 100 km/300,000km/sec equals 1/3000th of a second. Is that a reasonable reference frame for 'instantaneous'?
I have seen various estimates for how long an excited CO2 molecule holds onto the energy before re-emitting, from a full second to 1/100th of a second. So that is anywhere from 3000 to 30 times slower than instantaneous.
But wait. Some times the CO2 molecule gives up its energy by molecular collision instead of by reemission. At surface temperature and pressure there are roughly a billion collisions per second per molecule. Perhaps we need to redefine instantaneous. Of course collisions will add energy just as often as they subtract it at local thermodynamic equilibrium. Does molecular collision really count as losing energy if it is still there but just in a different form?
No it does not. Cooling, the loss of energy, only happens when photons actually leave the surface or atmosphere, and escape to space.
Any absorption of surface radiation slows the loss of energy to space and stores that energy in the atmosphere. It then has to find a way out.
CO2 absorbs and stores all the 15 micron radiation from the surface. Some, but not all of that energy migrates to a height in the atmosphere where CO2 can radiate to space and actually cause cooling. That takes time, lots of it. The surplus energy must find a different pathway out. The only available pathway is to return the energy to the surface, causing the equilibrium temperature to increase, which allows more radiation to be produced at wavelengths that can directly escape to space, bypassing atmospheric absorption altogether.