If Duke's is "the official mayo of the tailgate", then really anyone can make any sort of nonsense statements in marketing. The FTC's truth-in-advertising laws aren't really meaningful anymore, and I don't think they are applied equally to every industry (or at all).
So while the government could limit commercial speech, it also can't impose arbitrary restrictions without cause. There has to be a rationale that walks down the narrow definition that previous courts have defined. e.g. is it illegal, misleading (this is where we assume the case is), or does the government has good cause (public good, etc).
Being forced to disclose information is considered a more extreme restriction than being prohibited from stating something false. Lies aren't as easily protected as free speech as the truth, but in practice it's allowed as an opinion or if the receiver wouldn't take it literally (best in the world, top quality, etc). But compulsory speech has to have good cause and I think we'll see challenges when companies get annoyed by these new restrictions. And we do have mandatory disclosures for things like pharmaceutical ads (which shouldn't even exist). But I doubt that our courts will see AI as a threat to public good on the same scale as drugs, tobacco, and alcohol are (big mistake, IMO). And perhaps I'm cynical, but under the current regime I would bet that we'd see the courts blocking birth control ads before letting NY keep their AI disclosure laws.
The civil lawsuits will be flying though. Every time someone's shitty LLM uses the likeness of an actor's appearance or voice for some stupid ad, we can expect some lawyers to get involved. And that's regardless of whatever state laws might be around. If I were Robert De Niro or Taylor Swift, I wouldn't care if an ad says "this is AI" on it, I'd freaking sue if an ad looked like me or sounded like me.