Permaculture is a collection of tools we can use to improve the land, the harvest, the people, the planet...
But at it's heart, it's basically a tool kit and we take out the tools that are relevant to the situation.
Some landscapes and lifestyles don't include animal care. In other places, animals are a big part of improving the landscape.
Thinking about it another way, look at all the places around the world where people farmed on the same land for hundreds or thousands of years. Europe, Africa, Asia, parts of the Americas...
Some of these systems, like in England for example, included animals.
poop would be spread as needed, weeds or parts of the crop not considered edible for humans fed to the livestock, or if the field was in a fallow stage, we would graze the animals there to improve the soil.
In other parts, like some of East Asia, animals factored very little into soil building.
So yeh, animals are a part of
permaculture, for some and not for others. Here's the category where we talk a lot more about animals:
https://permies.com/c/critters
As for insurance, livestock doesn't normally come under pets. Try agricultural insurance.
Most livestock is home treated, so if you ever have to go to the vet, it's good to treat this as education and ask the vet all the questions "how do you identify this, what stage do we intervene, what stage is fine, what other treatment options are there...how to prevent it happening again"
Generally, the sad thing with livestock is that the worth of the animal is a big consideration. A hen can
sell for $25 in her prime, so if the vet bill will be more than that... um... we could just eat the hen. Most insurance companies feel the same way so insuring a
chicken as if it's a pet is a very bad bet on their end, so it costs the user more.
(of course, chickens are pets, they are lovely... but insurance and farming also takes into account the economic side)
That said, I will pay for a vet if it is something new to me on the farm as I need to know how to diagnose and treat if it comes up again - and more importantly, how to prevent it.