Like if there were still Neanderthals that had evolved alongside us.
Not just that, but we did the same with Denisovans in Asia, and in Africa there are high levels of admixture from a currently unknown photo-human, so yeah they are with us for sure.
The wiki on this is a fascinating read: https://en.m.wikipedia.org/wiki/Interbreeding_between_archaic_and_modern_humans
Just look out a window bruv.
Look in to prairie dog communication. Just sounds like dumb yips to us, but each little yip is full of information. Stuff like “Human with dog is approaching from 20 feet away.”
That is a fairly simple example, but it basically shows that the communication modes of other earthly species are so alien to us that we have no hope of comprehending them. The world could be filled with whole species of brilliant philosophic minds, and we just wouldn’t know it, but crows and dolphins are a good bet for sapience at least.
Also: Other Edens is a loose fit but might be to your liking. It does parallel worlds stuff, instead of having all the species be native here.
Major spoilers for books Terry Pratchett and Stephen Baxter wrote:
Yes! This is one of the main premises of the Long Earth series.
The Neanderthal Parallax is pretty close to what you're describing. Its about a portal being opened up to a world where Neanderthals were the dominant species, not homosapiens.
Perdido Street Station is not set on earth, but it feels like a very lifelike depiction of a modern multi-species society. The different species are not simply recolors of humans, and include insectoids that can't speak so they write or use sign language with outsiders and have extreme sexual dimorphism. despite the magical elements, it's descriptions of the repressive political system, racism, Suffrage lotteries, socialist movements, mutilation as punishment, prostitution and burgeoning bohemian artistic movement are pretty realistic.
13th warrior / eaters of the dead kinda gets into that. But it was also deliberately written as a retelling of Beowolf, so it's not exactly what you're looking for.
Those are the same novel btw, the name was changed at some point.