What is Elon Musk's actual role and authority within the Department of Government Efficiency (DoGE)?

While a federal judge sided with DoGE in a recent court ruling, she expressed skepticism about Elon Musk's role. The White House has clarified that Musk is not in charge of DoGE, but rather serves as a senior adviser to the President with no formal authority to make government decisions. This distinction is important as Musk has no official power to implement changes or make governmental decisions independently. The question of Musk's authority has become a contentious issue among Democrats, particularly those on Capitol Hill who have challenged his involvement in federal operations.