I think they trimmed the feathers way to short.
I think he is treating himself and the cut feathers. Pulling damaged feathers ( cut feathers) is a way to stimulate his body to regrow new ones faster. I think he will be ok.
But I do think he was trimmed incorrectly. Budgies can fly pretty well even with clipped feathers sometimes so keep him safe. I know you plan on letting them grow back in and allow flight do that's great.
I thought that as well but what’s done is done. Long term I want him to be able to fly around the house with supervision. But I cannot let him do that unless we can safely handle him. His feathers that are pulled out have barely any fluff left on the ends.
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Not trying to stir any pots, but my birds were allowed to roam in the small area we live in before they were hand tamed...simply control light and use a millet spray to get them back into a cage if needed...they don't really dig dark, so keeping the light in areas you want them is generally pretty effective. If they like millet, you can use that as extra motivation.