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

According to recent legal filings, Elon Musk serves only as a senior White House adviser without any formal administrative position over Doge. The White House clarified through an affidavit that Musk is not the head of the Department of Government Efficiency, comparing his advisory role to that of Anita Dunn who worked under President Biden. This clarification came in response to a lawsuit filed by 18 liberal state Attorneys General who challenged what they believed was Musk's unconstitutional role as head of Doge.