I’ve always thought of it as Palpatine let his guard down and revealed his true appearance.

He was physically consumed by evil long before the prequels took place, but he used the force to hide his appearance and appear younger and healthier.

But doing so probably required at least a tiny bit of constant focus. So when he was in his weakest moment, about to be beaten, he lost that focus and his true form emerged.

Then he was able to use that to his advantage by saying the Jedi did that to him, and it made the senate feel sympathetic towards him. It also meant that he didn’t have to be constantly drawing from the force to hide his appearance; which, lets face it, sounds like a hassle.