I wouldn't use pre cooked chicken for soup.
Plus the food that's used in a grocery deli is the usually food that's about to become unsaleable due to age, according to a recent Reader's Digest. Same with cooked haddock, too, in the meat section, btw.
I pressure cook a fresh bird, with salt and spices, cool on a plate (briefly in freezer for speed, if needed), then strip. I use the cooker water as a base, and add some California (lowest arsenic) brown basmati rice, usually with some canned garden heirloom tomatoes, and simmer, adding the vegetables part way through, and the cooked meat last. I leave the tasty, nutritious, and healthful fat in. It's really not soup; it's chicken stew. The rice will absorb water and thicken it.
I usually use onions, carrots, celery, and one frozen jalapeno, adding the carrots 1st, then the celery and then the onions. I add the jalapeno, after slicing, with the rice.
I generally use sea salt, black pepper, tumeric, paprika, allspice, garlic flakes, and a touch of Ceylon cinnamon, which is milder and sweeter than the more common grocery variety, which is Cassia. I bought a pound from Amazon, and use it in/on several things, such as my canned homemade pink (cooked with skins, with some picked out before canning) applesauce, from my backyard tree (Macs), with no pesticides. What a taste difference the skins make, and they add nutrients, too!