This does look like a prolapsed vent, which usually happens after the hen lays an egg and their oviduct does not retract again, and can prolapse further instead. There are a few factors in causing this, like laying stress, obesity or low calcium, but no hard and fast rule to prevent the issue in laying hens. I don't think its anything to do with soaking in the pot, except that was your opportunity to notice. And it helps to clean and soak the tissue to help it go back in, as well.
If it were me I would monitor the hen closely for any complications, checking to make sure the tissue remains un-prolapsed, and consider probably isolating her to a clean dry place to see if it happens again over the coming days, especially after laying. Other chickens pecking at her is a danger. If the prolapse happens again there are many good sources on possible treatment, here is
one from a wound-care product maker. The prognosis may be bad or good but is usually better when you notice it early on.