My understanding is that an egg that sweats simply has more moisture than it needs and it’s trying to get rid of it. @noodlehaus had an egg (she named the hatchling Leaky) that survived a similar ordeal, and so did @allytheant with her little palmetto baby in this post. Ally’s egg wasn’t leaky, but it did get moldy.
As for me, I had a couple eggs do the same thing around the same period of development last year, and unfortunately, the whole clutch went moldy despite my best efforts.
Suggestions that sometimes work:
(1) candle the affected egg(s) to see if there are veins, or if the embryo has already died (especially on the one that has changed color)
(2) give the eggs fresh air (still medium humidity) for about an hour
(3) sprinkle athletes powder on the affected area if mold develops (it appears that some have started to get moldy from your photo)
Things I changed for this year to improve my outcomes:
(1) Use vermiculite (I no longer use perlite because half my clutches went moldy that year, and I heard from a friend that half their eggs went moldy, too, on the only year they used perlite).