What is Elon Musk's actual role in the Department of Government Efficiency (Doge)?

According to a recent court filing, Elon Musk is not the head of Doge as previously perceived, but rather serves as a senior White House adviser without any formal administrative authority over the department. The government compared his advisory position to that of Anita Dunn who worked under President Biden overseeing various management areas. This clarification emerged in response to a lawsuit filed by over 18 state Attorneys General who had challenged Musk's role, alleging it was unconstitutional because they believed he formally headed the department.