It sounds like he is very young. He may just be really young and hasn’t had time for his feathers to grown in completely. He was probably too young to be weaned and away from the parents, so watch him carefully and make sure he is eating. A lot of breeders who breed in volume, will pull the chicks out of the nest boxes as soon as the oldest chick looks old enough. But this can mean the youngest in the clutch is not weaned yet. Most of the time the chicks will see the older ones eating and learn to eat out of desperation. But not all of them do, and those chicks do not survive unless the store that bought them notices. But if they got them in and sold the bird right away, they might not notice a chick isn’t eating yet.
If the tail and wing feathers do not continue to grow, the chicks could have a virus that affects parakeets and other parrots. You should notice growth daily, and his tail and wing feathers should be full length in about 2 weeks, maybe a bit more. But if they keep looing stunted after a week or two, the bird is most likely sick and you should take him to a Vet or back to the pet shop. But I think he is probably super young and needs extra care to make sure he is eating.
Thank you for asking Lafeber,