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Where is the constitution does it say the state can't do that?
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We would ask you to rephrase - and, if we interpreted correctly, to reread.
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"We"? Yeah, okay, Your Highness.

As for the content: the law says what it says. Where in the constitution of the United States of America and its amendments does it say that a state government must be truthful about public health statements?

The law says what it says. A behavior might be rotten, evil, illegal under other documents, and an all-round bad idea and still not a violation of, in particular, the constitution of the United States of America and its amendments

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The gp points out that some states, (for example, Massachusetts) opt to put this in their own constitutions
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But not Mississippi evidently, or the court probably would've mentioned that and Mother Jones reporter Sophie Hurwitz would've mentioned that in the article. Maybe Mississippi should enact some kind of state constitutional provision asserting this, but they haven't.
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