Anthropic has vowed to fight this designation in court.
Without weighing in on the constitutionality or legality of the move, I think it's obvious that this kind of retaliation power is unmatched by any private business that has a contractual dispute.
If a private business doesn't like Anthropic's terms, it can walk away from the deal, but it can't conduct coordinated retaliation with other companies before ending up in antitrust territory or potentially violating the Sherman Act.
Now for my editorializing: The fact that Pete Hegseth is willing to apply this type of designation against a U.S. company simply because he doesn't like its terms is pretty chilling. It's all the more scary once you consider which terms he objects to.