Refactor API structure: move chat functionality to v1 router, implement dependency injection for OpenAI client, and set up application state management

api/dependencies.py

@@ -0,0 +1,7 @@
+from fastapi import Request
+from openai import OpenAI
+
+
+def get_llm_client(request: Request) -> OpenAI:
+    """FastAPI dependency – returns the singleton OpenAI client from app.state."""
+    return request.app.state.llm_client