Who handles project management with a freelancer versus an agency?

With a freelancer, you are the project manager. You define the work, track progress, manage scope, coordinate with other contributors, and catch problems. This is fine if you have the time and the skill, and a problem if you do not. With an agency, project management is included: a dedicated project manager runs sprints, tracks progress, manages scope, and is your single point of contact. If you do not have engineering management of your own, the agency's project management is a significant part of the value, and a significant cost a freelancer engagement pushes onto you.