The only mention of the Stefan-Boltzmann in the first 31 years of the UN IPCC Assessment Reports occurs in the 6th (2021). The law is implicit in some drawings showing environmental heat flow, especially those showing the upward emission of IR from the surface. However, it is never—repeat NEVER—applied to predicted future surface temperatures. Doing so would expose the folly of most (if not all) climate models.
The sole mention of the equation is in reference to the “Planck Response,” a negative feedback phenomenon. Importantly, it applies to a disequilibrium situation where the heat radiated to space is greater than or less than the heat absorbed from the sun, and tends to hold the surface temperature constant at a set point determined by the solar flux, the albedo, and the greenhouse effect.