The metrics that will help a Product Owner determine if a product is delivering value are customer satisfaction and time to market. This is because:
Customer satisfaction is a measure of how well the product meets the needs and expectations of the customers5. It reflects the value proposition of the product and the feedback from the users.
Time to market is a measure of how quickly the product can be delivered to the market. It reflects the agility and responsiveness of the Scrum Team and the ability to deliver value early and often.
Other metrics, such as productivity, velocity, and percentage of scope implemented, are not directly related to value delivery. They may indicate how efficiently or effectively the Scrum Team is working, but they do not necessarily reflect how valuable or desirable the product is for the customers or stakeholders.
References:
Professional Scrum Product Owner™ Training, page 5, section “Product Value”
Professional Scrum Product Owner™ Training, page 6, section “Product Vision”
Professional Scrum Product Owner™ Training, page 7, section “Product Backlog Management”
Professional Scrum Product Owner™ Training, page 8, section “Release Management”
Professional Scrum Product Owner™ Training, page 9, section “Business Strategy”
Professional Scrum Product Owner™ Training, page 10, section “Stakeholders & Customers”