They have not; a social media post does not satisfy the requirements of 10 USC section 3252.

They are required to notify Congress (they have not), prepare a report with specific sections (they have not), and the reasons must fall within a set of categories outlined by statute (this does not).

There will be a court fight and they will lose, just like they lost the tariff battle, because of poor competence.

(Trump's post on Truth Social was actually fine. He said the USG would stop doing business with Anthropic, which is within its legal right. Hegseth's follow-on post is the problem. It is possible that Trump did not expect or want Hegseth to do that, that this was meant as bluster to bump along the negotiations; Hegseth has a recent history of stepping out of line within the administration and irritating people like Rubio.)

If the USG can mandate that everyone who works for a company that ever took a federal contract be genetically engineered, then I think they can tell people to not use Claude.