The product owner is responsible for preparing and maintaining the product backlog, ensuring it accurately reflects user requirements, priorities, and acceptance criteria. This role acts as the voice of the customer, maximizing product value by managing backlog items, ordering them to reflect business priorities, and clarifying requirements for development teams.
Monitoring stage progress (A) and managing project-level risks (B) are typically roles of the project manager or risk owner within PRINCE2 governance. The project backlog (C) contains higher-level requirements for the entire project and is not the product owner's direct responsibility.
The product owner bridges business and delivery, ensuring the team works on the most valuable features while maintaining clarity and quality of backlog items.
Reference: PRINCE2 Agile Foundation Version 2, Section 5.2 "Roles and Responsibilities," and PRINCE2 Agile Study Guide, Chapter 5.

The Delivering level is responsible for the day-to-day management and decision-making within the constraints set by the project manager. Delivering teams carry out the actual work to create the project products and manage their activities under the project's governance framework. The Project Manager manages the overall project, while directing sets the strategic direction and commissioning authorizes initiation.
This separation ensures clear responsibilities and empowers the delivery teams to self-manage within defined boundaries.
Reference: PRINCE2 Agile Foundation Version 2, Section 3.4 "Project Management Structure," and PRINCE2 Agile Study Guide, Chapter 3.

The assess step involves evaluating the probability and impact of identified risks to determine their severity and prioritize them for management. This step is crucial for effective risk control and helps allocate resources appropriately.
Planning relates to defining how to manage risks, identification involves discovering risks, and implementation concerns applying risk responses.
Reference: PRINCE2 Agile Foundation Version 2, Section 8.3 "Risk Management," and PRINCE2 Agile Study Guide, Chapter 8.