What are the key skills and experience needed for managerial roles?

Experience with being in charge and having to coordinate people, especially against high expectations and having experienced individual and collective failure.

As for skills, that should be about having an understanding of what the people or processes one is managing do and how they do it, in principle.

Further, skills around the tools used in that line of work such as office and project management tools go a long way, as do skills around stakeholder management and people skills. In particular knowing how to negotiate and say no to people, even those who hold power over you, is essential for success.

Knowledge of statistics and other basic data and math skills are very helpful as well.