Which type of engagement would be the most appropriate to assess the maturity and rigor...

A due diligence engagement is the most appropriate type of engagement for assessing the maturity and rigor of the organization-wide risk management process of a target entity that management is considering acquiring. Due diligence involves a comprehensive appraisal of a business undertaken by a prospective buyer, especially to establish its assets and liabilities and evaluate its commercial potential. It typically includes evaluating financials, operational processes, and risk management frameworks to ensure informed decision-making about the acquisition.References:

The Institute of Internal Auditors (IIA), Practice Guide on Due Diligence

"Mergers and Acquisitions: A Step-by-Step Legal and Practical Guide" by Edwin L. Miller, Jr.