Linking your previous thread here just for the convenience of readers who want to refer to it:
https://ball-pythons.net/forums/show...ythons-urinate
I don't know what responses drinking soapy water would cause, but I would expect them to be entirely digestive issues. I've only had one eggbound snake, and it did not present at all like what you're describing. I don't think that internal parasites would cause such a distinct shift in behavior and appearance.
My suspicion would be a toxic response to the insecticide. Among the symptoms in human toxicity are respiratory symptoms, coordination issues, tremors and convusions (source). Symptoms in snakes are muscle tremors, disorientation and paralysis (source).
Even after a cage cleaning, permethrin is stable on surfaces, so the repeated applications may have simply built up. Soap and water don't remove it well; it is used on human clothing for insecticidal purposes and lasts through a handful of machine washings. It might be that the repeat applications weren't fully dried when the snake was returned to its cage (I would expect there was a bit of a logistical issue with having to have the snake out of its enclosure during the cleaning process and things might have been a little rushed, which is understandable). You say "opened the lid" which suggests a top opening enclosure; it may be that limited ventilation plays some sort of role as well.
Given the repeated soaks and excessive urination, it may be that the snake simply took on way too much water and is hyponatremic. Soap might break down the skin's resistance to water (which is probably pretty low in short tailed pythons to start with -- I would expect they have a high rate of evaporative water loss). This is just speculation, though, and a vet would have a good idea as to whether overhydration is a factor based on symptoms.