Me again... here’s some more pics:

Wrong soil for over watering. Soil is great if you never over water but that's why we use cactus soil mixed half with perlite. Once rot sets in, it is most deadly to the crown where the growth comes from. However, it usually sends up new sprouts (pups) that will continue to grow. Best guess from me is to let it continue to dry out and leave alone. If the soil is still damp, remove from pot onto papers and let totally dry out before placing back into pot. I wouldn't try to re-pot now because the stress is already too great. Cut off all the rot you can. Bright light and warmth will help out. Best of luck.

Wiggle the foliage and if it comes off easily it means the base is rotted. You can also stop watering altogether til spring and see how it fares. They are very tough plants but once rot sets in, no salvaging.

Thanks so much bossyvossy and stush!