Yeah there kinda isn't any good ones rn, Monster Tails got close but that game really does not know what it wants to be, it feels really stuck between whether it wants to be the Anime, the Manga, the Games, or... Fate? for some reason?. I'll come back to you if I can think of anything, but im coming up blank, at least right now. I haven't checked out Animon and I've heard good things about it, so maybe check that one out? and even then it seems to be more "you have one partner animon". idk its a difficult space for ttrpg design, I think you could wait for the Tactics based PTO to come out, and I've had friends joke about a TSL mon catcher game but one of those takes too long and the other one is a joke.
oh ig there's also the 30 year old joke game Pokethulhu but im 100% sure thats not what you're looking for