Add unified constructor mechanism to MCP TS API to allow client injection

Summary

Enhance the TypeScript MCP API (excluding files under the legacy folder) by implementing a constructor mechanism that allows for an optional client to be injected. If a client is provided, the API should use the provided client to perform the corresponding database operations. The current API interfaces should remain functional, ensuring backward compatibility.

Details

• Implement a mechanism in the MCP TypeScript API that accepts an optional client object in the constructor.
• If a client is provided, use it for all subsequent database operations within that instance.
• Maintain all existing APIs, so consumers who do not provide a client will experience no breaking changes.
• Exclude all files under the legacy folder from this enhancement.
• If feasible, consider designing this mechanism in a unified way across all relevant classes/modules, but this is optional.

Motivation

Allowing client injection improves testability, customizability, and flexibility for advanced users without disrupting existing consumers.

Acceptance Criteria

• The MCP TypeScript API can accept an optional client in its constructor (excluding the legacy folder).
• If provided, the API uses the injected client for all operations.
• Backward compatibility is preserved.
• Enhancement is implemented in a unified fashion if possible (optional).

This issue is written in English to facilitate Copilot Agent comprehension.