That's part of the recurrent confusion with this administration. In previous administrations, including Trump 1, people didn't need to spend a ton of time thinking about what it means to make a legally effective proclamation, because there was a baseline of competence. When a government official announced "We're doing X", they would do so as a summary of a large amount of legal process with the intent and effect of causing X to be true. If you went to challenge it in court of course, you'd have to identify some specific action as the label, but everyone would understand that this is a formalism.
Here, Hegseth has simply made a social media post. He did not publish any official investigation which led to the report. He did not explain what legal power would permit him to impose all the restrictions the post claims to impose. There is not, five hours later, any order on an official government website about it. So we have a real question. If a Cabinet secretary posts "I am directing the Department of War to designate...", does that in and of itself perform the designation, or is it simply an informal notice that the Department of Fascist Neologisms will perform the designation soon?