Is there any such paint as compleatly nontoxic paint with no scent?

A good low VOC chalk based paint is the Vintage Market & Design brand. Water based, virtually odor free ( I paint furniture indoors in winter- no issues) and 72 colors. You can find them online. High quality, low cost!

When I repaint my house, even using low voc paint might be a problem, so I plan on relocating the pets for at least a week. When I did my mom's house many years ago when low voc paints were starting to become available and cost a bloody fortune, I took her pets for 9 days. Even if you change flooring it can create havoc with pets, so happy you are watching out for your feathered baby. I always try and make changes during spring or fall when I can have all the windows and doors open to air the place out faster.

Check with a good Paint store... there are "low" and "no" VOC paints... recommended for those with allergies , especially babies and little kids.

https://www.poison.org/articles/2013-dec/paints-for-indoor-use

I was told by a painter and 2 paint stores, that the darker the colour the more VOCs there are likely to be in the paint.

Acrylic and latex are water based. That's basically all we can get here now for walls. and it's all I use.

Although I really like Sherwin-Williams, the last one I bought smelled for quite a few days, but there was no window, just an exhaust fan. The colour was about the 3rd one down on the paint strip (from lightest to darkest).

I agree with venting: windows, fans, and possibly relocating your parrot, until the smell dissipates. Chemicals are in just about everything: flooring as mentioned and fabrics (curtains, upholstery, carpeting).

https://www.benjaminmoore.com/en-us/interior-exterior-paints-stains/quality-begins-with-chemistry/asthma-allergy-friendly

I've never used it.