[AI-8] PLU-584: add api for chat streaming

[kevinkim-ogp]

TL;DR

Added a new chat API to stream LLM responses from Pair based on user inputs.

What changed?

• Created a new /api/chat endpoint that handles streaming chat responses
• Added Langfuse integration for prompt management and observability
• Set up feature flag integration with Launch Darkly for prompt configuration

How to test?

1. Send a POST request to /api/chat with a valid authentication token
2. Include a request body with the following structure:

   {
     "messages": [
       {
         "role": "user",
         "parts": [{ "type": "text", "text": "Your message here" }]
       }
     ],
     "userId": "optional-user-id",
     "sessionId": "optional-session-id"
   }

3. Verify that the response is streamed back

[kevinkim-ogp]

Warning

This pull request is not mergeable via GitHub because a downstack PR is open. Once all requirements are satisfied, merge this PR as a stack on Graphite.
Learn more

• [AI-11] PLU-605: chat feedback #1352
• refactor: AI form modal #1311
• [AI-10] PLU-604: Preview steps and create Pipe #1310
• [AI-9] PLU-603: Chat interface #1309
• [AI-8] PLU-584: add api for chat streaming #1307 👈 (View in Graphite)
• [AI-7]: setup api route for chat streaming #1306
• [AI-6]: add ai related deps for frontend #1305
• [AI-5]: create pipe from generated steps #1304
• [AI-4] PLU-595: frontend to enter prompt and generate steps #1303
• [AI-3] PLU-583: (backend) mutation to generate AI steps #1302
• [AI-2]: Bump typescript and eslint deps #1301 : 1 other dependent PR (#1312 )
• [AI-1]: Install deps and bump zod #1300
• trunk/ai

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[linear]

PLU-584 AI: Generate markdown first then generate JSON