fix(web,api): fix WebSocket authentication for chat real-time connection (#547)

Co-authored-by: Jason Woltje <jason@diversecanvas.com>
Co-committed-by: Jason Woltje <jason@diversecanvas.com>

apps/web/src/components/chat/Chat.tsx

@@ -89,7 +89,11 @@ export const Chat = forwardRef<ChatRef, ChatProps>(function Chat(
     ...(initialProjectId !== undefined && { projectId: initialProjectId }),
   });
 
-  const { isConnected: isWsConnected } = useWebSocket(user?.id ?? "", "", {});
+  // Use the actual workspace ID for the WebSocket room subscription.
+  // Cookie-based auth (withCredentials) handles authentication, so no explicit
+  // token is needed here — pass an empty string as the token placeholder.
+  const workspaceId = user?.currentWorkspaceId ?? user?.workspaceId ?? "";
+  const { isConnected: isWsConnected } = useWebSocket(workspaceId, "", {});
 
   const { isCommand, executeCommand } = useOrchestratorCommands();