Scratch is often around 7-8% protein. It diminished ALL nutrients including protein and importantly the amino acids.. Making SURE to keep treats below 10% of total daily intake is usually the suggested limits..
Layer feed is usually around 16% protein.. and is considered the minimum to keep a light bodied layer in laying condition. Most birds will benefit from 18-20 ish % protein full time..
Using a grower or flock raiser with oyster shell free choice on the side is a good choice for many flocks. Noting that SOME feathers may not grow back in until molt.. "Feather Fixer" is essentially the SAME thing but with more ouster shell mixed in.
If higher protein or nutrients are required.. using a chick starter )OS on side for layers) or turkey starter would be much wiser choice than cat food.. Sometimes I buy game bird pellets and use that as a treat, win win.
An EE got into my stag pen/bachelor pad.. she was taking SO long to grow in the feathers that were plucked that I spent funds for the vet to make sure it wasn't depluming mites which are microscopic.. even though I wasn't seeing angry red skin or other symptoms.. just needed to make sure I wasn't missing something..
Patience.
Dry skin.. be sure you're not adding DE to the dirt bath (it allegedly works by making micro cuts and dehydrating pests in some dry environments).. the surface is the epidermis.. it's okay for that to be a little as they have no way of exfoliating. The deeper layers of the dermis are likely more "plump" for lack of a better word.
Others have hit the nail on the head pretty well.. nutrition and protein/amino acids are essential to all aspect of immune system and health including feather production.
Genetics whether a fast feathering or slow feathering bird MAY be impacting growth rate!
Stress impacts everything. So if she's still being bullied.. even without actual plucking..
A supplement like Rooster Booster brand Poultry Booster (product) or Rooster Booster brand Poultry Cell (product mixes best with moist food not water).. are GREAT pick me ups on OCCASION.. no supplement should be given more than 10 days in a row.
I just realized you're is AU.. you might not have the products mentioned available.. so please use the information best ya can!