When Neera Tanden assumed a role as senior adviser at the White House last week, after her bid for a Cabinet post went off the rails, it was viewed as a consolation prize. In reality, Tanden may have just stepped into a more quietly powerful position: entering President Joe Biden’s inner sanctum and avoiding the scrutiny from her detractors that would have come with a more public-facing role. As senior adviser, Tanden is now among a small, select circle of advisers in the White House. She’s included in daily briefings. She’s one of a half dozen senior advisers and one...