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

According to a recent court filing, Elon Musk is not technically part of Doge but serves as a senior advisor to the President, similar to Anita Dunn who worked under President Biden. The White House clarified that Musk has been tasked with overseeing Doge employees on behalf of the president, but has no formal administrative role over Doge or any part of its operations. This clarification came in response to a lawsuit filed by 18 state Attorneys General who alleged Musk's role was unconstitutional. The government's filing specifies that Doge employees are being onboarded at respective federal agencies as political appointees, while Musk remains in an advisory capacity without heading the department.