Sometimes, succulents may create a callus line, thus effectively protecting the healthier side. But it all depends how deep and far along the rot has set in.
So that was the reason I was asking if that orange part continues to feel soggy. If so, as last measure, then slice off all the rotted part and, apply a light dusting of cinnamon as fungicide, keep it warm and air dry it for as long as it takes.
It will be a long wait and risky just because it is winter. Be very patient, and good luck