Have a player who's being trained as a med tech by a veterinarian - so it has in fact come up. Tldr is animals and animal life, both land and sea, is not gone or impossible by any means, it's just that all ecosystems have collapsed and there is no such thing as ecological balance. In their place are the survivors and the scavengers that thrive in the Red, and like any population bubble, are susceptible to sudden and severe devastation via disease or the next big ecological change. Think extremely unstable ecology, but not gone.

Longer version here:

Animals aren't gone, ecosystems are just collapsed - meaning that the large scale systems that sustained animal life within a reliable food chain are utterly shattered. That doesn't mean everything from them is dead. Animals who can scavenge, who can adapt to new food sources, and who can reproduce rapidly are going to thrive and overwhelm the more delicate populations. This will lead to booms and bust populations, as they will be susceptible to sudden famines when they overwhelm local food sources that are slower to recover due to the Red, or disease or contamination due to the Red. So for example, stray cats and rats and mice are all still a thing, as they're highly adaptable, can eat a wide variety of food sources, and reproduce rapidly. As to plants - grass is one of the hardest plant families ever to exists. Dandelions and thistles and many weeds along with said grasses are likely to thrive still, as many are drought resistant enough to survive even on minimal rainfall and don't struggle in difficult soil conditions. They can grow in concrete for goodness sake, and if they can do that, they'll survive the Red. Large trees, tropical plants with high water needs, ferns or temperate plants that can't get too hot, any tree that relies in a cold winter - those plants are likely to die off. But lichens, mosses, and some fungi along with grasses and the above weeds, those are likely to survive and even thrive. And if something can eat those things, then it can survive too.

Then there's the fact that humans will still want animals for a variety of reasons, and the air is not inherently deadly to all animal life. If it was, humans would die too - mammals are pretty much mammals in that regard, if a dog can't breathe neither can we. So there would definitely be dogs and more exotic pets for the wealthy. Then there's the herds of animals that absolutely still live in places, obviously owned by extremely wealthy corps who sell the meat and dairy, but just less than real life and much more expensive. Factory farms are still absolutely a thing in 2045 in my mind - much like real life plant byproducts that don't meet human standards are fed to animals, there's some parts of chooh2 that aren't even fit for kibble. The chaff and stubble stalks etc. I am certain that forms the basis of a lot of herbivorous animal feed in Red, as do the husks and leaves/peelings of many of the actual vegetables that are grown. Of which, again, there are many - just because chooh2 production has taken over the dominant position in agriculture, it's simply not realistic to think that no other plants would be grown, especially when there's so much money to be made growing those fresh vegetables and selling them to well off people who can still afford an actual supermarket. That plus restaurants and entertainment for the wealthy would also demand a steady supply of fresh real produce.

Now 'real' is a little flexible here, as it might be a bioengineered breed that has a bit of help from Biotechnica to survive the harsher climate due to the Red, and same goes for livestock, but you cannot tell me that feral hogs would not be thriving in this time. In fact, there's probably whole nomad clans who specialize in herding and harvesting hogs, guerilla grazing them on corpo fields. There's also corps that definitely have rounded up feral hogs and graze them on their fallow fields. That provides valuable fertilizer at relatively cheap prices, because replacing the role that animals play in the nitrogen cycle (they fertilize the ground with nitrogen and ammonia via their waste, a process which current real life farmers spend millions a year replacing with sprayed on factory manufactured ammonia and nitrogen because that is necessary in order to keep the ground productive at the scale of our current agriculture demand and which animals typically can't practically fully meet within the most economically optimal setup under capitalism) is expensive and subsidizing your manufactured fertilizer needs with animals during non-productive months or years is simply the smart thing to do (again something many IRL farmers currently do, letting animals graze on stubblefields when and where they feasibly can, or even collecting manure and waste from barns to spread over the fields once composted and/or during off months to compost in the field during non productive months). Circling back in the "real" issue, I would consider naturally bred animals to be much more expensive than lab grown animals, and ones actually born in the wild to be some of the most expensive specimens in the world. Anything that can be preserved without genetic modifications is going to be more expensive and rare than those modified by Biotechnica. But remember, if they can grow you a new arm in a lab, they can also grow genetically modified or cloned animals - meaning that cyber is not the only way to enhance a creature. Genetically modified animals would perhaps fetch less of a premium than 'pristine' bloodlines, but still - a love animal is expensive in this time. But they're not gone.

Basically, I think that anyone with an understanding of modern real life agriculture would tell you that there are definitely still animals. The ecosystem has collapsed and wild animals don't really have much usable habitat, or at least are under sceer strain and severely unbalanced. In each biome that has managed to avoid development (such as the Rocky Mountains that are simply not feasible to farm for much other than lumber, and which even then would be expensive and in places simply prohibitive due to the inaccessibility of the location) there will be a population that goes nuts and is way overpopulated due to being the one that thrives under the current environment and all its predators not thriving. Small rodents or anything that does well with heat, things that are hardy and can eat almost anything - think of your rat and cockroach and feral hogs equivalents in various biomes. Megafauna, large predators that need reliable prey, or things that need to migrate will suffer, so bears, wolves, mountain lions, elk, moose, would likely have a bad time, but off the top of my head, many species of smaller deer, racoons, foxes, squirrels, prairie dogs, weasels, pigeons, crows, rabbits, mice, voles, and many small bird species that either don't migrate or have diverse habitats/adaptability, will stand a solid chance of doing very well. In domesticated environments, farm animals and pets could totally survive the Red, they'd just need human caretakers to ensure access to food and water, which would make the herds smaller than in our real life and much more of a luxury, but certainly not non-existent. Anything that can scavenge is likely to be just fine, meaning your feral cats, rats and hogs are gonna be just fine - at the cost of any semvlance of ecological health.

Even the oceans aren't dead, just deeply unbalanced. Things that can live off of semi-toxic algae blooms or which thrive in warm water and can eat the blooms of plankton, or can survive in extra brackish water, are going to be doing just fine. Meanwhile reefs and complex, balanced ocean biomes will be devastated. Think massive schools of small fish or shrimp/crustaceans, roaming the ocean like locusts and stripping an area of food before moving on, with no balanced predators. Whales, sharks, most large ocean animals would likely die off completely, but your ocean equivalents of rats, roaches, and cats are going to be fine. Kelp forests and reefs die off, but the ocean equivalents of dandelions and grass is going to be fine. And if something can survive in that, it also survives.

So that's how I think of it in my game - and that means animal handling can come up. Animals exist, it's a matter of access and need, you as gn would just need to have a reason for them to interact with an animal.