The direct answer for a cockatoo
It is not safe for a cockatoo to eat food made for other kinds of pets, even though a cockatoo is physically capable of eating almost anything it can hold. Cockatoos are large, long-lived parrots whose natural diet of seeds, nuts, fruit, blossoms and roots is far leaner than the concentrated fat and animal protein in dog and cat food. The fact that a cockatoo enjoys raiding another pet's bowl, and will return to it daily once it learns the trick, is exactly why the answer has to be a clear no backed by management, not an occasional shrug.
A clever bird makes this a household problem
A cockatoo problem-solves at a level few pets match. It can unscrew, pry and chew its way into food storage, memorise where the dog is fed, and time its raids for when the bowl is full and the room is empty. Its beak crushes kibble pieces that would defeat smaller parrots, so size offers no protection at all. Cockatoos also turn successful theft into a game with an audience, screaming with delight and throwing pieces around, which tends to get the behaviour laughed at and repeated rather than stopped. Treating the setup, storage, feeding places and supervision, as the fix is the only approach that works with a bird this determined.
What carnivore food does inside a cockatoo
A cockatoo's system handles fat in measured amounts from nuts and seed, but dog and cat foods deliver fat, salt and protein at densities meant to fuel mammals that burn far more energy. Regular helpings push a cockatoo towards obesity and the liver strain that follows in large parrots, and the vitamin loading in a mammal's premix, eaten on top of the bird's own balanced diet, can overshoot nutrients that are harmful in excess. Wet and raw pet foods carry the heaviest risk, because bacteria multiply in a bowl standing at room temperature, and a cockatoo feeding from it also meets the other pet's saliva and whatever the food has collected from the floor.
When a theft needs more than tidying up
One raid on dry kibble by a healthy cockatoo usually needs nothing more than removing access and offering the bird its normal food and water. Escalate to an avian veterinarian if the cockatoo ate wet, raw, mouldy or long-standing food, if it ate a large amount of anything rich, or if you then see regurgitation, a change in droppings that persists, unusual quietness in a normally demanding bird, or any breathing difficulty. Cockatoos mask illness behind noise and display when they can, so a bird that stops performing and sits withdrawn is giving you information worth acting on the same day rather than the same week.
Feeding arrangements that outwit a cockatoo
Feed dogs and cats in a room with a door the cockatoo cannot open, at set times, with bowls lifted and washed afterwards. Store all pet foods in hard, latched containers inside closed cupboards, because a cockatoo reads a flimsy lid as an invitation. Give the bird's own meals structure and interest in return: measured pellets or a quality large-parrot mix, vegetables and fruit at set servings, and foraging devices that take real effort, so the day's food challenge happens in the cage rather than at the dog's bowl. Supervision during out-of-cage time in shared rooms closes the last gap. KinsLe's Kinny is a useful first call when a cockatoo has beaten your arrangements again, helping you weigh what it ate and what to watch for while the facts are fresh.