feat: add gateway module with FastAPI server (#5)

* chore: add .claude/ to .gitignore

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* feat: add gateway module with FastAPI server

- Add new gateway module with FastAPI app for API routing
- Add gateway and serve commands to Makefile
- Add fastapi, httpx, uvicorn, sse-starlette dependencies
- Fix model config retrieval in lead_agent (support both model_name and model)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

---------

Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>

backend/src/gateway/app.py

@@ -0,0 +1,64 @@
+import logging
+from collections.abc import AsyncGenerator
+from contextlib import asynccontextmanager
+
+from fastapi import FastAPI
+from fastapi.middleware.cors import CORSMiddleware
+
+from src.gateway.config import get_gateway_config
+from src.gateway.routers import models, proxy
+
+logger = logging.getLogger(__name__)
+
+
+@asynccontextmanager
+async def lifespan(app: FastAPI) -> AsyncGenerator[None, None]:
+    """Application lifespan handler."""
+    config = get_gateway_config()
+    logger.info(f"Starting API Gateway on {config.host}:{config.port}")
+    logger.info(f"Proxying to LangGraph server at {config.langgraph_url}")
+    yield
+    logger.info("Shutting down API Gateway")
+
+
+def create_app() -> FastAPI:
+    """Create and configure the FastAPI application.
+
+    Returns:
+        Configured FastAPI application instance.
+    """
+    config = get_gateway_config()
+
+    app = FastAPI(
+        title="DeerFlow API Gateway",
+        description="API Gateway for DeerFlow - proxies to LangGraph Server and provides custom endpoints",
+        version="0.1.0",
+        lifespan=lifespan,
+    )
+
+    # Add CORS middleware
+    app.add_middleware(
+        CORSMiddleware,
+        allow_origins=config.cors_origins,
+        allow_credentials=True,
+        allow_methods=["*"],
+        allow_headers=["*"],
+    )
+
+    # Include routers
+    # Models API is mounted at /api/models
+    app.include_router(models.router)
+
+    # Proxy router handles all LangGraph paths (must be last due to catch-all)
+    app.include_router(proxy.router)
+
+    @app.get("/health")
+    async def health_check() -> dict:
+        """Health check endpoint."""
+        return {"status": "healthy", "service": "deer-flow-gateway"}
+
+    return app
+
+
+# Create app instance for uvicorn
+app = create_app()