Did you ask the vet for a tube feeding kit? It may be time to get a little nourishment into her to see if she's merely starving or if she's starving due to another issue. We won't know until after you tube feed and see if it improves the lethargy.
This is a process of elimination since her...
The poop indicates she's not eating. While chickens can go a while without food, they can quickly lose strength, then they lack the will to eat. Also, not eating may also risk dehydration. Tube feeding can intervene and keep a chicken from the tipping point into starvation and the downhill slide...
It's unusual but not unheard of for egg binding to go unresolved for this long. I had a hen go nine days with a prolapse and obstruction. It turned out not to be an egg, but tissue from an egg. Once it was passed, the hen bounced back to normal immediately.
You may not see an egg. If it's...
The skimpy poop is another indication of a blockage. Give her another calcium tablet. Wrap her in a towel securely to confine wings and feet. This also calms the chicken. Then pry open the beak by using a fingernail to get the beak to open enough to slip a finger into the side to hold it open...
There is a chance this behavior is egg related. She may be struggling to lay an egg. It's been my experience that a shell-less egg can cause a hen to feel "off", probably because the egg doesn't move at the rate of a regular egg, so the hen may be feeling "backed up". Try giving her one tablet...
I see nothing in that poop to indicate bacterial infection, presence of parasites or toxin exposure. You could still have a sample fecal float test run by your vet, but It's doubtful it would show pathological levels of parasites.
That leaves one of the most common causes of "off" behavior...
Poop holds important clues when a chicken is behaving "off". When you get a poop sample, photograph it, post it here, and describe it with words to make up for the missing dimension.
You might also contact your local vet and ask for them to run a fecal float on the poop sample. It is...
"Heading out" meaning gone for a week or gone for the day? It might make a difference if this hen is coming down with something, and her behavior does indicate that.
What does her poop look like? If it's watery with streaks of mucous, she might need an antibiotic.