The purpose of the Plans theme in PRINCE2 is to provide a framework to design, develop, and maintain the project's plans. This theme ensures that the project plans are aligned with the project's objectives and facilitate effective management and control of the project throughout its life cycle. References: PRINCE2 Foundation manual, PRINCE2 official resources

Explanation
Reference https://www.prince2.com/blog/the-7-principles-themes-and-processes-of-prince2/

The Benefits Management Approach in PRINCE2 is designed to outline how and when the improvements (benefits) delivered by the project will be measured and to define the reason for delivering these improvements. This approach ensures that there is a clear understanding of the project's intended outcomes and how these will contribute to the organization's objectives, thereby justifying the project's existence and ongoing investment.
PRINCE2 Foundation Manual

The Project Initiation Documentation (PID) is the base product against which the Project Board can assess progress, issues, and ongoing viability questions in PRINCE2. The PID includes key documents such as the Business Case, the Project Plan, and risk management information, providing a comprehensive reference for governance decisions throughout the project. References: PRINCE2 Foundation manual, PRINCE2 official resources