But clickety click, Barba Trick: it's not formally a department, so there is now law stopping the president from creating this informal advisory thing. It's not clear exactly what it is. But they just put the word "department" in the name and ran with it.
What may be illegal is when this advisory "thing" starts getting access to various important cogs of the government and intimidate federal workers by leveraging the fact that the president apparently can just fire federal employees who are in 'policy-influencing' positions.
That's again one of those cases where the law may not be ready to counteract blatant abuse because historically so much has been up to democratic norms, and here we have a clique that is using norm violation as their battle cry