Add API Documentation for `/api/chat` Route

[babblebey]

The API routes in this project currently lack proper documentation. To improve usability and developer experience, we need to document the /api/chat route, ensuring that contributors and users understand how to interact with it.

This documentation can be implemented in one of two/both ways:

1. Swagger UI Auto-generation – Automatically generate API docs with OpenAPI/Swagger UI.
2. README Documentation – Manually document the route usage in the project's README.md.

Initial Focus: /api/chat Route

The /api/chat route should be the first to be documented, with an emphasis on how it can be consumed using the [useChat](https://sdk.vercel.ai/docs/react/use-chat) component from Vercel AI SDK (@ai-sdk/react).

Key Information to Include:

• Endpoint: POST /api/chat
• Request Body: Structure and required fields
• Response Format: Expected output
• Usage Example:
  • How to consume the endpoint with useChat from Vercel AI SDK
  • Example integration with a React component

Next Steps

• Decide on documentation format (Swagger UI vs README).
• Implement documentation for /api/chat.
• Extend documentation to cover additional API routes in the future.

Relevant Files:

• src/app/api/chat/route.ts
• README.md (if adding manual documentation)
• Any new files for Swagger/OpenAPI setup (if chosen)

[babblebey]

Putting this article here as resource I found in generating document for apis in next.js - https://catalins.tech/generate-swagger-documentation-next-js-api

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