Ohio could possibly sue him civilly because of the bomb threats that caused them to shut down schools. That’s the best I got.
If anyone is hurt over this, then they likely have standing for a civil suit (see Alex Jones).
Criminal it’s definitely more tricky. Trump will likely get away with telling his followers to storm the capitol, so I doubt “eating cats and dogs” comes close to the same standard.
Once upon a time, admitting to something like this would have been an impeachable offense. But that’s long sailed as something Congress would fairly enforce.
Here’s the thing, Vance didn’t make up the story, a Nazi did. I’m guessing Vance is now claiming responsibility because lying about the origin is better than the truth, that he’s just repeating lies from self avowed Nazis.