I am sorry I wasn't online earlier to see your posts, and equally sorry you felt you had to delete them. I am not an expert by any stretch, but I have a hen that has prolapsed 2x's, and is now in recovery for her second. I didn't see the picture you posted but if it looks anything like mine, it's very very distressing. The good news is that hens are incredibly resilient.
The first time, our hen had an egg bound and another one came down and broke. We soaked her in a warm tub and the whole egg came out. We ended up poking and prodding to help her expel the broken pieces. It was AWFUL. I thought for sure she'd die. She would sometimes close her eyes in pain. But fortunately, we got most of it out. When it was over, she had really a fleshy mess. We kept her in a small dog crate mostly in the dark - maybe 2 or 3 hours a day in various time spans with water and food. In 8 days the mess dropped off and her vent returned to normal.
A month later she had another egg bound but we could not get the egg to move over and out. It was awful, but the vent was clear, although on the outside, if you can picture it. Within a week, the mess fell off and her vent returned to normal.
So if you are still reading, the hard part will eventually fall off. We kept it moist and somewhat clean with a spray bottle. I occasionally put Prep H on it, and sprayed it with an antiseptic. It's important you keep her vent clean so she can poop.
I know how hard it is to hang in there with sick birds. If they weren't pets, I'd figure out some way to end her misery, but she seems to pull through. We are not putting her back in with the other chickens. I think she wasn't getting access to the calcium (oyster shells) because she rarely went outside the coop both before and after the prolapse. So we built another coop and will put her in there with a couple of our other odd ball chickens that need extra help.
hang in there. I am going to give you links to the thread that helped me and my own threads. Keep me posted.
my thread:
https://www.backyardchickens.com/forum/viewtopic.php?id=596204
And when no one responded to my second plea for help I posted this thread which includes a photo
https://www.backyardchickens.com/forum/viewtopic.php?id=611143
here is the thread about someone else's chicken, Rosey
https://www.backyardchickens.com/forum/viewtopic.php?id=580399