Kai: So how can “pet animals” benefit from permaculture and homesteading?
For some, there are obvious benefits, and others, it may take a little creativity.
Dogs and cats have been kept on farms since forever, they can play vital roles in pest control and protection of livestock, and in turn, may glean from the leftovers of a butchering.
Rabbits, guinea pigs, and other pet rodents can often get enrichment from fresh garden goods and hay. Many of these animals must chew to keep their teeth healthy, and so fresh branches from nontoxic species of trees and shrubs can easily be provided for free.

Birds, both fowl and exotic can also be provided with branches for chewing or perching. Branches with bark still on them helps to prevent foot problems, unlike dowel perches still found in petstores, which promote bumble foot.
Birds benefit from fresh foods, and food variation. Mulch, fresh hay, or open bottom aviaries can also aid in natural stimulation of behavior, preventing boredom and destructive behaviors.
For my parakeets, I even make hanging toys with leather and safe woods, which I clean and drill holes in to be able to string them on the leather.

Although I don’t have as much experience with reptiles, I can at least say that my turtles probably benefit the most from living this natural lifestyle. They are practically wild in their diet and environment, aside from their Winter abode that is set up inside. I would one day like to experiment with more reptiles to see how natural of a life the “permaculture” ways can offer, but for now, if you look up “ecosystem terrariums” there are some pretty cool things people are already doing in the pet reptile community.
So far I have successfully kept several different breeds of goldfish, and guppies in outdoor ponds. Both have even bred off on-site food. I do not buy fish food, and never will. Most have far too many toxins which slow the fish, and make the water dirty very quickly.
Duckweed, earthworms, pill bugs, hard-boiled egg, wrigglers, water fleas, and blood worm will take care of these fishes’ needs to the point of multiplying.

As an end note, almost any pet animal can get a boost in health and mental stimulation from being in the fresh air, getting sunlight, and eating a variety fresh foods. There are too many ways to cure boredom in animals if we just allow them to behave naturally, all we have to do is offer them safe, alternative opportunities to play, dig, chew, run, fly, or explore!