This is my "guess" I'm not a vet nor an expert, so bear with me - I'm not good with technical terms.
To me, it looks like "egg matter" or coagulated exudes - possibly the beginnings of reproductive problems. Salpingitis (inflammation of the oviduct) comes to mind and then maybe later on Egg Yolk Peritonitis.
If you know which hen this came from, I would keep a close watch on her. Vet care is always best, but if she were mine, I would consider treating her with an antibiotic since, to me, this is a sign that she has some type of infection. Tetracycline, if you can get it would be my first choice. If not, then I would try Tylan50.
Caught early, antibiotics can help, but are not a cure all, so she will need to be monitored.
***warning Necropsy photos!****
What you found in your egg, though a lighter shade, reminds me of coagulated "egg matter" that can be found in hens with reproductive problems-note the matter is darker, but has been "cooking" in the abdomen for some time.
https://www.backyardchickens.com/threads/egg-yolk-peritonitis.1154532/#post-18103856
Just my thoughts on this - I really hope that I am seeing things differently and all is well.