Help with schema design
If your interest is explicitly to keep track of the direct manager of the employee, then the simplest solution may be to add manager_id to the project table, and populate that from employee.report_to when a project row is created. It's not worth setting up a full-fledged history mechanism just to track this specific relation.

If, on the other hand, this is intended to allow anyone to track down the projects they or their subordinates (at any level) started while they were their subordinates, then you'll need a full history mechanism. Check out the link mustaccio noted in the comments, to the question Best way to capture historical changes between levels in a dimensional hierarchy.