There is some evidence that it's generic. Darwin, as I mentioned, pointed out the close commonality of domesticated animals: the floppy ears, neoteny, year-round breeding, piebalding or spotty colors etc. There's no reason to expect all the human domesticators to be selecting for stuff like floppy ears, so the repetition suggests that there's some universal domestication syndrome where those all come as a package. I think the existing GWASes tend to support this but aren't definitive? Not really an expert on the details there. (One interesting claim is that humans appear to have undergone a light form of domestication syndrome too.)