Does role of "Agile Project Manager" exists in scrum?

The roles of Scrum are defined in the Scrum Guide, and there are only three of them - Scrum Master, Product Owner, and Development Team member. There is no role in Scrum called "Project Manager" or "Agile Project Manager".

That said, there are certain skills associated with a project management role or bring a project manager - proposing projects, managing scope, managing budget, scheduling (milestones and deadlines), stakeholder analysis, risk management, and others - that may be useful in an organization using Scrum. Rather than being encompassed in a single role, these are shared to varying degrees among the members of a Scrum Team and to the organization that the Scrum Team exists in. There may be some value in organizations having experts in project management who have these skills and can support a Scrum Team and the organization in various ways.

Most Scrum Masters I've worked with are former project managers. The problem with this is that these new Scrum Masters are focused on facilitating meetings and on tracking work in a management-mandated tool, and running reports in this tool. They run Daily Standups (annoyingly called DSU) and not Daily Scrums. They don't understand mentoring, they leave the training to "Agile Coaches" and don't have the right skills to be a coach.

Most Scrum Masters I've worked with are former project managers. The problem with this is that these new Scrum Masters are focused on facilitating meetings and on tracking work in a management-mandated tool, and running reports in this tool. They run Daily Standups (annoyingly called DSU) and not Daily Scrums. They don't understand mentoring, they leave the training to "Agile Coaches" and don't have the right skills to be a coach.

It depends on the mindset of each individual person... But maybe some of the former project managers should consider to work as PO and not as SM.