As a part of monitoring and controlling the project, the project manager should update the risk register. The project manager should update the risk register with information on risk reassessment…

Actual costs and schedule delays are general project performance metrics tracked in the project management plan and performance reports - the risk register captures risk-specific outcomes, not broad schedule or cost variances.

Assessing how well the team performed their risk management duties is the purpose of a risk audit, not a standard risk register update entry.

Capturing only the actual cost of risk events is too narrow - PMBOK requires capturing outcomes of the risks themselves and the outcomes of the planned responses, not just financial impacts.

PMBOK specifies that Control Risks updates the risk register with actual outcomes of risks and the actual outcomes of risk responses, enabling the project team to close out risks, document lessons learned, and provide future projects with empirical data on risk response effectiveness.