Hopefully, she is done with all of the lash material. Poor thing must have been in a lot of distress. Sounds like you are dealing with her problem. Looking forward to hear if she is doing alright this am.
I will be here for a little while. @Wyorp Rock stays up a little later. Hopefully, your hen will get a little rest in that quiet spot for the night. Just check in, and maybe offer her some fluids. But she really needs some calcium or Tums if there is another egg or lash egg coming. Azygous stay...
The darkening on the one end of the lash egg is due to it being exposed to air and drying out, I think. So glad that she was able to pass that. Hopefully, the swelling will go down. If you have any hemorrhoid cream or hydrocortisone cream, that can reduce swelling. Honey or sugar plus a few...
Keep her vent lubricated with ointment or honey. She could have another lash egg behind that, or is uncomfortable. I would,still give the calcium or a Tums tonight.
Here is some info about why hens lay lash eggs:
https://www.bhwt.org.uk/hen-health/health-problems/lash-eggs-salpingitis/#:~:text=The infection is referred to,McKillop DVM MSp VM DACPV).
https://the-chicken-chick.com/salpingitis-lash-eggs-in-backyard/
Just saw the picture when I posted. Yes, it looks like that may be lash egg material from salpingitis, an inflammation of the oviduct. Is the vent opening enlarged? Keep it moist, and let us know how it goes.
Azygous has dealt more with a prolapse than I have. Does the yellow mass seem like a lash egg stuck in the prolapse? I would give the calcium soon as possible. Keep the vent and prolapse area moist with ointment, oil, or honey. Let us know how she gets along.