Hi! I am having a blast with this game but had huge trouble finding the animals at first. I found that there wasn't a guide for that yet, so I decided to create one so I could help other people find animals as well! If you know of any animals I might've missed, please tell me in the comments! I'll add them.

A few base remarks about animals:

• Each animal is clickable only once. That is, you can click multiple different seagulls, but you can't click the same seagull twice.
  
• When looking for animals, especially if you only start doing it when you've already put down a couple hundred tiles, it's best to zoom as close as you can, or just one step less close than that. Some animals are easy to miss or hidden well enough that you need to view them from multiple angles!
  
• According to the game announcements in may 2023 the developers had added or would shortly add cows, rabbits, chickens and goats. I have not encountered these in-game, so they might not have been added yet. If you have seen them in your game, please let me know!

Cats can, as far as I've found, be found on three places: on buildings (such as the marketplace, palace, etc.), on tractors and on boats. They come in several colors and poses.

Boats
Boats are fairly straight-forward: the cat will likely be at the front of the ship, and every true ship (so no canoes) that spawns on the map will have one cat.
Example of a cat on a ship

Tractors
Those tractors you see being driven around your farm fields? Yeah, they're controlled by cats. Just as straight-forward as the boats: each tractor the map spawns has one cat.
Example of a cat driving a tractor

Buildings
Buildings are a little more tricky, since the actual place varies depending on the building, as well as the amount. You will likely need to look at a building from different angles to find the cat!
Example of a cat in the local bell tower, showing that you sometimes have to look carefully!

Most buildings have one cat, whose location seems to not change in different playthroughs, though I feel like the amount of cats is not fully set in stone.
Some (but not all!) two- and three-star-buildings, seem to generally have two cats.
Monuments seem to have three cats on average.
Example of the great castle, which actually has three cats!

Catless places
There are a couple of places that you might expect to have cats that do not. So far these places seem to be:

• The zeppelins
  
  
  
  
  
  
  
  
  
• The geysers

There are several birds in the game, but only two seem to be clickable:

Seagulls
Seagulls can be found... in the sea. They sit on poles or buoys in pretty much any water, but usually in the bigger waters.
Example of several seagulls on buoys and posts

Crows
Crows look pretty much the same as seagulls, except they're black and they're found in the fields. Also, they aren't on buoys, just on poles. They do seem to be more rare than seagulls? Or my fields just aren't big enough.
Example of a crow sitting menacingly on a pole

Yes, there are frogs! They seem to be able to spawn pretty much everywhere where there's water, and sit snugly on lilypads.
Example of a couple of frogs

Of course, there are also many animals in the game that you can't click! See the examples below:

Fish
Those big fish you sometimes see swimming in the water? Yeah, they aren't worth any points.
Big-ass fishies

Migrating birds
The birds that fly over the map in a V-formation are very pretty, but also not clickable.
Pretty geese

Insects
The fields in pan'orama are fortunately a bit more insect-filled, but those pretty butterflies are not clickable, nor are the bees and wasps.
Beautiful butterflies and bees