I'm sorry that your question wasn't answered in a timely manner. It's important to note that once a budgie acts ill it's already quite ill and in need of the attention of an avian-oriented vet (please see here: theparrotsocietyuk.org/veterinaryadvice/avian-vets). This is a protective mechanism because sick birds are attacked by other birds in the wild. His symptoms of fluffing (an attempt to conserve heat), somnolence (sleepiness), inappetence, diarrhea or polyuria/increased volume of urine (?) are all important symptoms but they're not pathognomonic (specifically indicative) of any one particular disorder. They’re signs of “sick bird syndrome” - part of an array of highly nonspecific clinical signs.
An avian-oriented vet might first treat symptomatically and supportively by providing supplemental fluids and electrolytes by needle and tube feeding a "recovery" food. Blood tests and cultures of his choana - the slit between his oral cavity and nose - and cloaca (vent) may be taken. Whole body X-rays can be quite helpful as well.
Until he can be attended to, please heat up his environment to 29.4C by means of a 100W bulb shined into his partially covered cage (not at night when he needs to rest) or by taping a heating pad set on its lowest setting to the sides of his cage. If he appears weakened remove his perches and put his food and water on the bottom of the cage along with him. Add a water soluble avian vitamin such as Oasis brand to his water at half of the recommended dose so as not to make his water distasteful. Add a calcium supplement such as Calcivet or Calciboost to his water. These supplements are available in pet/feed stores. Avoid over the counter antibiotics designed to be placed in his water. They won't be effective if only because an ill bird won't drink enough to medicate itself properly.
Nutritional imbalances are a common cause of illness in our pet birds. What has his diet consisted of in addition to the stick and millet, please? Seeds should compose less than 20% of his diet. A diet of mainly seed and nuts has excessive fat, carbohydrates, and phosphorus; marginal protein; adequate vitamin E, and are deficient in amino acids, calcium, available phosphorus, sodium, manganese, zinc, iron, vitamins A, D3 (necessary for efficient absorption of calcium), K, and B12, riboflavin, pantothenic acid, choline, and available niacin. Ideally, a balanced pelleted diet such as can be found here: www.harrisonsbirdfoods.com or here: www.lafeber.com/pet-birds should be fed as well as hard boiled egg yolk, pancakes and cornbread, the tops of fresh greens, dairy products such as yogurt and cheese, fresh fruits such as apples, pears, melon, kiwi, and berries, vegetables such as broccoli, carrots, beets, asparagus, cabbage, sweet potato, and squash, and even tiny pieces of meat.
Unless I'm trying to acidify the crop in an attempt to manage bacterial or yeast overgrowth in a "sour"/impacted crop, there's no value to apple cider vinegar (acetic acid). Probiotics may or may not be helpful but they won't be harmful. Please respond with further questions or concerns if you wish.