Product Management Leadership Position
Question: "Is product management a leadership position?"
No, it is not. Product management is a strategic position.
There are mid-level and executive management roles in product management, e.g. the director of products and the Chief Product Officer (CPO), but these are managerial roles.
Leadership is the ability to influence others to change their behavior without having authority over them. So a leadership capability is a personal trait that an individual may have but it is not a characteristic of the product management profession.
The idea of product managers managing without authority is a notion that belongs to the legacy and unsupported Generalization approach to product management (product manager does everything, aka CEO of the Product).
For more information, see the Product Manager as Product CEO? article.