Which animals do you think humans would live most harmoniously with, or already are living with (mostly), without making them into livestock?

Cats IIRC are essentially wild animals still, yet we share our homes with them.

Do you mean without also making them pets? Because living harmoniously kinda implies a lot of interaction.

But, in general, any social animal can get along with another when there's no competition involved. The critters that tend to be pets that are good pets are all social or semi social. So are the best livestock, which can also be pets, but tend not to be as often because of habits or traits that make properly living with them difficult.

But, if you exclude pets, we already live closely such squirrels and have very little direct impact on their lives in the way of individuals on a daily basis. Nor do they cause us problems very often. They can also be relatively friendly with a bit of effort, though it isn't a good idea.

Crows are great neighbors unless you're a farmer. They don't cause a lot of trouble, and they're unlikely to let us bother them long. But they do go after crops a good bit, so you'd need good figurative fences with them as neighbors if you're growing food. Have to factor them in, or accept large loss. But if they hang around, they'll warn you of unfamiliar animals or humans, and they'll avoid messing with you for a minor bribe now and then. Fuck, crows are a mafia. They move in and start a protection racket lol.

Opossum here in the US are great neighbors. They won't mess with humans at all if they cab avoid it, and do us a ton of good vs ticks. They can get into garbage the way raccoons can, but aren't as messy when they do. Just make sure any crawl spaces are closed to them, and they're cool as hell to have around.

Deer can be nice to have around in the suburbs. Harmonious is a stretch, particularly for crops, but they're easy to scare off compared to crows. Pretty much non interactive though, which is actually ideal for wild animals.

Those are all animals that are fairly common outside of cities (and squirrels go everywhere) that already live relatively harmoniously with people.

Then you've got songbirds that are everywhere, with almost no interaction from their side. There's a ton of species that are around us all the time outside of cities, and sometimes in cities. But it's an almost zero contact kind of harmony, and we tend to do them more harm than good compared to the others I mentioned. So not really harmonious when they suffer from our presence a good bit. But, some of them can become friendly, which isn't all that common with mammals that we encroach on. You don't want to put out a coyote feeder, if you get what I mean.

There's stuff like bats where things would be harmonious as hell if presence wasn't so harmful to them as a whole.