In the last decade, it has been understood that the spectrum and dynamics of near-extremal black holes receive quantum gravity corrections that become large at low temperatures. These corrections come from a soft mode in the near-horizon geometry that is strongly coupled at low energies. In this talk, I will first explain how low-energy scattering processes in near-extremal charged black hole backgrounds are modified by these quantum metric fluctuations. I will then discuss how the black hole's probability distribution of energy level occupation evolves over time as it undergoes quantum-corrected Hawking radiation. Notably, the corrections to particle emission rates for charged black holes in a fixed energy or fixed temperature state were recently computed in arXiv:2411.03447. However, a near-extremal black hole prepared in a microcanonical or thermal state does not remain in this state as it radiates. Surprisingly, quantum corrections cause the black hole to evolve to a universal non-thermal state which is independent of the initial distribution and which exhibits a scaling symmetry not present in the semiclassical regime. This state gives new predictions for the Hawking radiation spectrum of evaporating charged black holes.