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Continue to offer formula twice daily but don't force him. Also, try offering it in a spoon instead of syringe. Also offer things like broken up cheerios, pelletized food for budgies (these are very small, millet size or smaller) and crushed millet seed. Don't forget to also teach him to drink water from a bowl or water bottle . You can do that with a water bottle by letting him nibble at the tip and get water.
You can encourage him to eat by spreading the things I suggested on a small towel and "pecking" it with uour index finger in front of him. If you have another budgie let him see the other one eating these things.
If you have a food scale weigh him every morning before feeding him to make sure he's maintaining his weight or not losing more than 2 or 3 grams. If he's losing 3 grams you unfortunately have to tube feed him formula.
The droppings also tell you if gets eating enough but body weight is much more accurate. If he passes droppings with tiny amounts of very deep green, almost black feces or feces with no form it means he isn't eating enough.
You would have to buy a feeding cannula or a butterfly catheter to put on the syringe. With a butterfly catheter you trim off the tubing about 2 inches from the attachment for the syringe. Draw food up through the tube into the syringe. Hold his head with neck fully extended and slide the tube down his right side of his throat to the crop at the base then push the syringe plunger.
Yes. Tube feed if can't get him eating by the other means.