When a project admin tries to reparent a project, they receive a "InsufficentPermissionError" error even though they are an admin for the project and the destination project.
This is caused when the project admin doesn't have admin access to the current parent project.
Since reparenting a project also affects the parent, it is considered a security violation to move the child project in this situation.
In this situation, it will be necessary to have a workspace admin or subscription admin reparent the project. Another solution is to grant additional permissions to the project administrator so they are an admin to the current parent project.