From my understanding, downloading and running software could be considered a form of conduct or could be considered a form of expression, depending on the intention (e.g. using an LLM to generate poetry would be expression). The latter would put it in a category that is covered by the first amendment. I'd imagine there would be quite an uphill battle to argue that using a specific LLM that has been made permissibly available isn't protected in some circumstances

There is ample precedent in Bernstein v. United States that it is, in fact, free speech, and none that ought to be revisited here.

AFAICT, there's a differentiation that should be made between the model and the mobile app. TFA, and I'm assuming the bill, too, AFAICT, don't differentiate. The model seems unequivocally speech. Whether a mobile app can be banned seems like a different question; from other reporting it seems like the mobile app is laden with lovely things like keyloggers, and there, I can see "national security" might withstand scrutiny.

If the Senator were actually concerned about American's data, he'd pass some privacy laws. But the GOP is all laissez-faire capitalists these days, and they would not want the government telling American companies that that can't sell American data for money.