Write API documentation and usage guide

[landoyjx]

Document the API in the project README or an API.md file. Include endpoint descriptions, request/response examples, error response formats, and instructions for running the server and tests locally.

Acceptance Criteria:

• Every endpoint has a description, method, path, parameters, and example request/response
• Setup and test instructions are clear and accurate
• Error response format is documented

Test Cases:

• Docs review: A reviewer can follow the README to install dependencies, run the server, and execute all tests successfully
• Docs review: All example curl commands in the docs produce the documented responses against a running server