Under your definition restaurants are public property and the government should have the right to ban smoking in them. Is that your contention?
And companies do not have rights under the Constitution, people do.
And yet they get enormous tax breaks unavailable to people. Go figure.
Generally property restaurants sit on are either owned by the restaurant or lease from private real estate investors. I can't think of a single restaurant where I live that sits on land owned by the government. I have no idea what they do "up nawth."
And "the people" tolerate it. Because they get tax breaks from the government doesn't mean they have the same rights as individuals. We can make up the loss for their tax breaks and they can institute tyranny as a big "thank you."