fix: use shared httpx client to prevent premature closure in SSE streaming

The proxy was creating a temporary httpx.AsyncClient within an async context manager.
When returning StreamingResponse for SSE endpoints, the client was being closed before
the streaming generator could use it, causing "client has been closed" errors.

This change introduces a shared httpx.AsyncClient that persists for the application
lifecycle, properly cleaned up during shutdown. This also improves performance by
reusing TCP connections across requests.

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

backend/src/gateway/app.py

@@ -19,6 +19,8 @@ async def lifespan(app: FastAPI) -> AsyncGenerator[None, None]:
     logger.info(f"Proxying to LangGraph server at {config.langgraph_url}")
     yield
     logger.info("Shutting down API Gateway")
+    # Close the shared HTTP client
+    await proxy.close_http_client()
 
 
 def create_app() -> FastAPI:

backend/src/gateway/routers/proxy.py

@@ -11,6 +11,31 @@ logger = logging.getLogger(__name__)
 
 router = APIRouter(tags=["proxy"])
 
+# Shared httpx client for all proxy requests
+# This avoids creating/closing clients during streaming responses
+_http_client: httpx.AsyncClient | None = None
+
+
+def get_http_client() -> httpx.AsyncClient:
+    """Get or create the shared HTTP client.
+
+    Returns:
+        The shared httpx AsyncClient instance.
+    """
+    global _http_client
+    if _http_client is None:
+        _http_client = httpx.AsyncClient()
+    return _http_client
+
+
+async def close_http_client() -> None:
+    """Close the shared HTTP client if it exists."""
+    global _http_client
+    if _http_client is not None:
+        await _http_client.aclose()
+        _http_client = None
+
+
 # Hop-by-hop headers that should not be forwarded
 EXCLUDED_HEADERS = {
     "host",
@@ -76,7 +101,8 @@ async def proxy_request(request: Request, path: str) -> Response | StreamingResp
     if request.method not in ("GET", "HEAD"):
         body = await request.body()
 
-    async with httpx.AsyncClient() as client:
+    client = get_http_client()
+
     try:
         # First, make a non-streaming request to check content type
         response = await client.request(