The primary role of the SM is not meant to “manage” the team or the project, but to guide the Scrum process and encourage self-organization. The Scrum Master has authority over protecting the team from outside influences, including from the Product Owner.
Whereas, the Product Owner role is to guide the vision and the development process through backlog prioritization and management. The Product Owner role has the autonomy over the product and its requirements.
The Project Manager role (if applicable) in Agile projects on the other hand, shifts from command and control to management of resources, risk and dependencies across teams and removing obstacles.