The way the skin on the neck looks bothers me. I would expect more redness, but the skin looks thickened, and I'm wondering about depluming mites. Those are microscopic and burrow into the skin at the base of feathers, and the irritation is bad enough that they will pull out their own feathers trying to get relief. Common areas are around the neck, on the breast and around the vent. A vet can look at a skin scraping with a microscope and ID them. Treatments are ivermectin or permethrin usually. Just throwing that in to cover the possibilities. (DE isn't going to help, and it can cause respiratory irritation to the bird and to whomever is applying it).
This is from Merck Veterinary Manual:
This is from Merck Veterinary Manual: