Do you have any hydrocortisone cream? Doesn't matter what brand. I've found it helps a lot when you have swelling in the tissue like this. I just treated one a few days ago that was similar (one of mine that has periodic prolapse

). I put the cream all over the tissue before pushing it back in, and add some more that I push in with my finger. The cream may seem like it doesn't want to stick, but keep at it, it will kind of dissolve in. If the prolapse won't stay in long, despite holding it in for a bit, then you can devise a sling/bandage to help hold it in longer, this has worked for me in the past. This thread in post #1 has some pictures of one.
https://www.backyardchickens.com/threads/successful-vent-prolapse-treatment-with-photos.1101406/
I use vet wrap/co wrap also. It may take a few tries to get it placed so that it will stay where you want it, and you may have to change it periodically, make sure you leave a poop slit. Every bird is a bit different in body shape, and in tolerance for wearing "accessories". My bird that prolapses periodically has had two tears in the tissue. Those formed scabs which made the tissue continue to get pushed out. Once it was healed enough that the scab could come off, the prolapse starts to stay in. The sling can help keep it in while healing so it stays moist. Sometimes a prolapse is a one time thing from an extra large, malformed oddly shaped, or rough shelled egg, and may never happen again. Sometimes it's a persistent issue and if it continues and gets worse over time, it may end up being the end of them. My current bird goes for long periods of normal laying between prolapses, this is her 3rd, so, for now, she's doing OK, but since she has a history of it, it may very well be the thing that eventually does her in. If you have birds that look alike, are hard to tell apart, I band the ones with issues like this, so I can remember if it's something that's happened before, or not. I just use multicolored zip ties. I currently have two banded for health issues, my prolapse bird and another older bird who is having crop issues.