Under the product features, you will notice this particular set is "non-stick". All non-stick cookware can kill you bird. It is easily identifiable by a black interior on the pot, pan or other cookware item, and the "non-stick" description. Avoid all cookware that isn't shiny, stainless steel. To clarify what is so toxic about non-stick here it goes: Non-stick cookware contains a product called "Teflon". When heated to high temperatures (aka on a stovetop or in a oven) Teflon releases odorless fumes that are highly toxic. As a human, our lungs are big enough that it doesn't tend to affect us, however in parrots, with tiny, sensitive lungs, these fumes can suffocate and poison the bird in a matter of minutes. There is no warnings or way to tell when these fumes are being released, and your bird can literally fall off it's perch dead. Even worse, after time, the Teflon coating will start to chip off on a microscopic level, releasing carcinogens in your food. It also has to be replaced every few years, because visible chipping will start happening, which ruins the cookware (and it isn't preventable).
Even if you don't own a bird, non-stick cookware is a terrible idea.
On the bright side, if you purchase traditional stainless steel cookware (which will cost a little more up front), there is no risk of it releasing anything toxic into the air or food, a good set of stainless will literally last a lifetime (my mom still has and uses the same set of cookware she got for her wedding 40 years ago!), there is barely any difference in the amount food will stick (non-stick is a big gimmick in my opinion), and when food does get charred on, it is easy to clean by boiling water, white vinegar and baking soda (all non toxic) in the item to restore it to shiny-new. For bakeware (because there is also non-stick items that go in the oven) always choose glass or ceramic. Just because it's inside the oven, doesn't mean it isn't releasing fumes if it's non-stick and we all know aluminum anything has been liked to alzheimers, so avoid cooker containing aluminum for your own safety.