What do budgie parents feed their newly hatched baby chicks?

If your budgie's parents are still around they will most likely care for them on their own. However if the parents aren't around or aren't caring for the babies properly, you will need to start feeding them yourself. Most pet stores will carry a basic baby bird food which has feeding instructions depending on your bird's age. You'll also need a syringe with which to mix and feed the food. As your bird grows you can start introducing an adult balanced diet to encourage them to begin eating more solid foods.

There are various recipes available online, usually these are based on products such as cereals for human babies, peanut butter, apple sauce and baby food (e.g. https://www.cuteness.com/article/make-homemade-baby-cockatiel-food). I cannot really recommend those, perhaps only as a last resort. If you can get commercial pellets for adult parrots and grind them with water (pre-boiled) to prepare a slurry, that would work, but the commercial formulae are better. Please note that the food should be at 40-41C and prepared fresh for each feeding.

As long as the parents are taking care of the hatchling themselves, you shouldn't need to do anything as they will keep it warm by laying with it in the nest, and feed it as needed. It also seems like you are feeding lots of nutrition-filled items to your birds as well! It is a good idea to have some baby bird food and a syringe on hand that you can mix up if you need to help with feeding, or if the parents aren't caring for it. Most pet stores carry this and will have feeding instructions on the side of the bag. Congrats on the baby bird! It sounds like it and its parents are in good hands.

You should just continue to feed your budgie a balanced diet that is designed for budgies. While spinach is a great treat, it should not be used as the main diet. If you are concerned about your budgie getting enough nutrients, you can add in some crushed oyster shells or a cuttle bone for calcium, or include some egg-food (a treat found at most pet stores) to help boost nutrition post-egg laying.

26 days is old enough that the babies should be starting to explore and eat some on their own. If only dad is feeding them he may be trying to encourage them to leave the nest and find food on their own. Making sure they have access to bird feed near where they can get to may help get them used to eating on their own and exploring some.

...without first speaking to a veterinarian since hand feeding babies can be tricky and possibly even lethal if you are not doing it correctly. If you cannot find a commercial formula, try the following recipe: -3 tablespoons of high protien baby cereal -1 1/2 tablespoons of wheat germ -1 1/2 tablespoons of millet meal -1 1/2 tablespoons of sunflower meal -5 drops of a multivitamin for birds. Blend all ingredients to a fine powder and then mix with warm water to a soupy consistency.

Momma bird may be a bit stressed out now that there are new babies to care for. Adding in extra food and water dishes so that each bird has one to eat at without fighting, and making sure both birds have their own perches to relax on can help reduce tension. As for the babies, momma bird should care for them herself, however having some commercial baby bird food (most pet stores will carry it) can be useful in case she can't care for them all on her own. As they get a bit older and start to explore, you can start to offer treats and pets to get them used to being handled.