RELAX!
If your chicken is pooping, things are fine, but you will have to get the purse suture taken out before your chicken lays an egg again.
This happened to my bantam cochin a few weeks ago. She had a terrible prolapse. Her hole oviduct was sticking out with a shell-less egg wrapped up inside. My vet bill was $450 though!
The vet anesthetized her, took an x-ray, cleaned her up, and examined her. Then she put in a purse suture to keep her insides on the inside. The x-ray did not show an egg in the oviduct. This is important because if there was an egg in the chute, it would need to come out in a day or two. My chicken stayed the night at the vet, and they made sure she was still passing urates and feces. If she could poop, it meant that the suture was loose enough. A purse suture is like a draw string on a bag.
Like your chicken, my chicken had some necrotic tissue where the prolapse had stopped circulation. She may have been prolapsed all day. I do not know because her cochin bustle tail feathers hid what otherwise was an obvious and ugly prolapse. The vet was worried but said "birds are amazing healers."
So, I brought her home and nursed her. She pooped as usual, but around 4 days in, the fibery broccoli leaves I was feeding her in addition to the scratch were getting backed up. She was till pooping, but not as much as I wanted. After a week, she definitely had a big turd in there. So I took her to get the stitch out, and an hour later she pooped a real nice big turd.
Also, a bit of necrotic tissue was sticking out. I pulled it gently because I thought it was an egg membrane. But then I could tell it was still attached by a small section. So I cleaned it, put K-Y on my pinky, and gently pushed it back in so it wouldn't be tugging on her healthy insides.
The next morning, she the necrotic bit came out again. So I went to clean it and push it back in, but it sloughed off.
I kept the chicken in for a couple more days for observation, then got her back outside in the coop. She is doing great now.
And today she laid her first egg since the ordeal, successfully! In her case, lack of calcium was the issue. Without a shell, it is hard for them to lay. She is still a young hen--she just started laying infrequently a couple months ago, and I think this is her first egg with a shell.
So, my advice is to make sure your chicken is pooping. If you know how frequently she was laying, you can predict when she will need to lay again. The purse stitch needs to come out before that. Or, after a week, whichever comes first. If she isn't able to pass urates and feces, the stitch needs to come out now.
But she will always be at risk of prolapse. So daily vent checks are needed. I am glad I started doing this with all my girls. I feel like we know each other better!