Add fastapi-langgraph-chat extension

[ulises-jeremias]

Problem

The LangGraph multi-agent chat proposal is useful, but it should not be a second full
FastAPI starter. It is an orchestration capability layered onto a FastAPI app.

It also overlaps with the simple chat extension if both define the same route shape.

Solution

Create extensions/fastapi-langgraph-chat compatible with fastapi-backend.

Scope:

• Add a small LangGraph state graph with typed state.
• Include simple nodes such as router, responder, and tool executor.
• Expose a route that does not conflict with fastapi-ai-chat unless explicitly
  intended; if it conflicts, define symmetric incompatibleWith.
• Include test-only fake LLM/tool implementations.
• Support native tools through typed functions.
• Leave MCP, RAG, and MLflow as optional follow-up extensions or documented
  integration points.
• Add docs:
  • template/docs/LANGGRAPH_CHAT_GUIDE.md
  • template/docs/README.md.append
  • .env.example.append
• Add partial pyproject.toml dependencies.

Constraints:

• No external LLM calls in tests.
• No frontend in the first implementation.
• No .github/workflows in this extension.
• Keep the graph small and readable; this should be a baseline, not a full agent
  framework.

Acceptance criteria:

• Generated tests verify graph routing and final response construction with fake
  providers.
• The guide explains how to add a new node/tool safely.

[ulises-jeremias]

This item is part of the MLOps roadmap. If you'd like to work on it, comment here.