I know man but I am kinda fascinated if more modern monster or even cryptids can be available to partner up and they would mesh with our classical youkai and the gumiho.
Most Cryptids count but would be a bit difficult to find/bond with. Due to being more modern monsters rather than ones from ancient mythology, such creatures don't have as much of a presence in the Human World or the...you know what fuck it. Sage didn't care about spoilering parts of his world so neither will I.
So, there's a secondary world filled with all the Monsters that show up in this Setting. No humans live there permanently and they've all basically formed their own societies and otherwise. Humans sometimes stumble into it/are sent there/get there through certain ways...but ones that aren't ready or don't know where they need to go usually end up either eaten or assimilated into the world itself. Human Souls aren't strong enough to resist the strong Spiritual Power emanating from the land and end up turned into Monsters.
Some monsters, like Brownies and otherwise choose to live in the human world instead. They keep their heads down to avoid detection. However, the older Monsters usually stay in the Monster World as a way to keep themselves alive by feeding off the energies of the land itself. In the past, the two Worlds were almost directly ontop of each other. Thus how Monsters were able to walk the same lands that humans did, and where most stories about them come from. But something happened that split the worlds apart.
Cryptids and such mostly remain in the human world. Usually because:
1. There's only one of them. Going to the Monster World is asking to be Ganked by stronger monsters.
2. They've gotten their own niches and lives in the Human world that they wouldn't be able to gain in the Monster World.
Edit: As for an Empathy Focused Partner Art:
1. Demon/Angel/Divine Creatures: Creatures that usually represent and feed off specific emotions. Not all are 100% like their biblical counterparts, but usually do look and act like them. This also includes things like Devas and Asura's from Hindu Myths and otherwise.
2. Ghost: Ghosts are basically big wells of Emotional Energy given Spiritual Form. They're usually connected to the world by strong emotions, so being able to read/effect them would fall under their wheelhouse. Mind you, they need to be Pure Ghost. Not Spirits/Ghost bonded to items like Yato is. Those are different.
3. Unicorn: Literally meant to represent Purity itself. Is it any wonder it's good with reading and understand emotions? Oh and if you don't want the regular kind, Kirins exist.
4. Cursed/Living Dolls: Unfortunately falling on the more negative emotional spectrum, cursed/living dolls would actually still fall under the same strong emotions wheelhouse as Ghosts and Spirits.