Hierarchical Data Reconstruction with Recursive CTE

Design a PostgreSQL solution to reconstruct a complete organizational hierarchy from a flat employee table with self-referencing manager relationships. Implement a recursive common table expression (CTE) that can generate a full organizational tree, showing reporting lines, hierarchy depth, and management paths. Include performance optimization techniques to handle organizations with 10,000+ employees, and provide a method to calculate organizational complexity metrics like average span of control and maximum hierarchy depth.