What is the constitutional problem with Elon Musk's role in the government?

The Constitution requires anyone in charge of a federal agency to be Senate confirmed, which Elon Musk is not. Though the Trump administration is now claiming Musk is merely a White House senior adviser with no formal role, this contradicts Musk's own public statements about 'deleting folks' in agencies and his apparent operational authority. This creates a constitutional dilemma in two ways. If Musk is acting as the head of DOGE (Department of Government Efficiency), it violates constitutional requirements for Senate confirmation. Even if he's working from the White House as an adviser while exercising substantial agency control, this still potentially violates constitutional separation of powers, as Congress passed laws establishing how these agencies should operate.