refactor: mount FastMCP app at /mcp and re-add /health to root for compatibility

src/monarch_mcp_custom/server.py

@@ -182,10 +182,14 @@ def create_app():
     mcp_app = mcp.http_app()
 
     # FastMCP.http_app() already includes its own health check and SSE routes.
-    # By mounting at /, we get /sse and /messages (FastMCP defaults).
-    # We can add our custom /health if we want it to be distinct.
+    # By default it uses /sse for the stream and /messages for POSTs.
 
-    return Starlette(routes=[Mount("/", app=mcp_app)], lifespan=mcp_app.lifespan)
+    routes = [
+        Route("/health", health_check, methods=["GET"]),
+        Mount("/mcp", app=mcp_app),
+    ]
+
+    return Starlette(routes=routes, lifespan=mcp_app.lifespan)
 
 
 app = create_app()