Did your hen recover from her illness? My husband and I just had to have one of our beloved hens put to sleep yesterday due to something similar but it sounds like your girl might be doing a little better than ours was. We know exactly what happened to ours because we luckily have a wonderful avian vet locally and we ended up taking her for an impacted crop surgery a few weeks ago and then just to be sure, we had a necropsy done at the UC Davis veterinary lab after the euthanasia. As I said, we had the obstruction (she consumed a bunch of straw) removed from our hen's crop but she had more straw material stuck in her GI tract. Nothing could pass the obstruction so she couldn't poop (we only saw white urea and very little feces, similar to your picture) and she would eat very little. It sounds like the crop of your hen isn't impacted but I'll tell you what happened with ours. After the crop surgery she perked up immediately. The avian vet had her on 3 oral medications (antibiotics, metaclopramide and lactulose) and near the end when she started to backslide we switched to intramuscular injections of metaclopramide and oral papaya enzymes once we realized the medicine was not getting thru the obstruction. It sounds like it's possible your girl may have an obstruction further down but it may not be as impacted as ours was.
If you don't have a vet as an option for you I'll share what our vet told us can help a hen pass an obstruction - papaya enzymes and metamucile, twice a day. You use the human chewable papaya enzyme that you can get at the drugstore, one chewable pill mashed up and mixed with 1cc water given orally every 12 hours - same for the metamucile... Mix it up and give 1cc twice a day. Make sure you get the real sugar variety and not sugar-free. Keep doing that until she has a normal poop. If she's not eating and losing weight, you should consider keeping her inside or warm because they burn a lot of energy trying to keep warm.
The last thing the vet said we should check for in the necropsy is metal poisoning from lead or zinc oxide. She said it's a very off chance but she has seen it once before and it caused the same symptoms as an obstruction. She noted that if the chickens had access to areas where lead based paint might be in the soil or if she could have picked up a piece of hardware. This was not the case for us but something for you to consider.
I hope this helped but mostly I hope your hen is fully recovered or improving!