Countless parrots have passed from most appliances heated and coated with PTFE but according to Phoenixlanding there safe, but should not be used around birds.
I agree that you should not get another bird right now. In time, if you move into a larger home and can place your bird in another room, shut the door and open all windows and use stainless steel cookware without any hidden PTFE then everything should be fine as long as there is not hidden gas leaks from the stove. Also, over heated oil and butter can kill your bird there respiratory system is so delicate.
The only cookware I believe is safe to use is stainless steel but now there hiding PTFE inside, you would have to call the manufacturer. Copper is safe and also cast Iron.
Never use the self cleaning button on a stove or cook with bags. There’s is so much to learn, I tried to sum it up in a small paragraph.
I lived in a small studio around 12 years ago in Hawaii and never cooked inside. I lived there for about a year then I moved into a larger 3 bedroom home.
the first thing I did was cook. I opened all the windows, placed them in there bedroom
and made spaghetti.
Even now, I rarely cook and my stress levels go up when I light the stove but I make sure the fans are going and a lot of air flow. I also have a rabbit air hepa and Voc filter going 24/7 in there bedroom. I believe that rabbit air has helped a lot.
If you need any resources, I would be happy to help you. Before you purchase any heated appliance, I would call the manufacturer ask if there is any PTFE, PTFO or PFOA’s in there cookware.