See the website DogFoodAdvisor.com where they rate the quality of most all commercial dog food, canned and dry.
I agree with you that most shelters can't afford to feed good food. I've rescued 2 gsds and both were fed cheap, low
quality food at the shelter and their body and coat looked bad too.
As soon as I upgraded their food and started adding eggs, vitamins, good meat, they looked terrific in a few weeks
and had a sparkle in their eye.
You might want to check with your vet in case your puppy needs worming.
Welcome to the forum and if you have any pictures, we love pictures.