You can sand off the worst of the paint, and there are paint on products like evaporate-o-rust that will remove all rust. It will leave pits if they are there. Then you can use a spray or brush-on rust converting paint. Rustoleum maks one - look for the words rust converting. The paint has a compound that chemically reacts with rust to form an iron oxide that does not rust any further. Otherwise the rust will keep,growing under the new paint. You do want to take off as much surface rust as you can. Even a wire brushing is enough. Then the paint can reach all the rust molecules. Once the paint is fully cured it's safe.
Saving older Powder Coated cages have merit. That said, the reality of 'sand blasting' the cage, cleaning and prepping the cage frame for Powder Coating is extensive work. Then following with adding the Powder Coating and placing it in the curing oven all added costs that exceeds what the owner wants to expend. Unless you own this equipment, cost exceeds the replacement cost of the cage.
Now, if that cage is a rust bucket, its time to trash it and move on! If you are dealing with minor spot (rust) problems, the time and cost maybe worth it.
Prior to beginning the process of buying the supplies, etc... A judgement needs to be made as to where the wear and rust problems are and whether they are from poor original application, cleaning or habitual grinding by your Parrot. If you determine that repair area is from habitual grinding by your Parrot that area should not be repaired as whatever you put on that spot will be ground-off again. For those areas that are defined as poor original application and/or cleaning, these areas can be repaired.
Please assure that you follow the process and products provided above. If you fail to halt the rust problem, you are wasting your time and money. So, do it right the first time! The final coating paint is to provide a cover for the sealing work you have completed and to blend the 'spot' repairs to the overall cover of the cage. Do Not Paint Over Powder Coated Surfaces!!!
There are a ton of paints on the market that claim all kinds of safety for 'everyone.' But, the only one that I have come across is "Amy Howard" At Home series finish coat paint. Please understand that the safety of the paint commonly does not include the Color /Tint that is added to it!
In closing, we are talking above spot repair in specific areas that are not caused by grinding actions of your Parrot! Painting over an entire cage is NOT recommended as painting on Powder Coated surfaces will flake-off.