Thank you for thatWell there's your picking solution then. He's trying to tidy himself up and flight feathers that are clipped it makes the ends of where they were cut catch on each other, very annoying to the birdie, He knows his wings aren't sitting properly on his back either and any tiny little spikes will be driving him batty as they disturb other feathers when he moves his wings around.
The check nibble he did is normal preening behaviour hopefully as those flight feathers moult back in and he has them all back again all what your seeing will have gone and he will just be sorting the tiny little barbs that hold the tiny little lines of feathers together out. See diagram of what I am trying to explain reference the barbs and how they work now think of it being snipped int he middle of the shaft (quill) half way down and how annoying it is not to be able to sort it all out and keep it all staight and in top condition so you can fly.
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The diagrams and your description makes sense.
But my dad has 2 budgies down stairs and they are not clipped and they do the same thing.
So just a little confused