Governors can issue executive orders. But like Presidential executive orders, they usually follow along existing laws without really breaking any. In this case, though, it seems to run contrary to freedom of speech… PLUS for a state to indicate official solidarity with a foreign nation most definitely seems to overstep the Fed, as it makes New York State appear to be behaving as a separate country from the USA altogether.
Can they do that? I don’t know… but it doesn’t sound like they can.