feat(web): SPA de chat (React + Vite + Mantine v9)

Cliente web sobre el gateway (REST + SSE). El navegador no habla NATS ni
cripto: el peer Go del gateway lo hace.

- Pantalla de conexión: gateway URL + identidad (persistidas en localStorage).
- Navbar: crear room (con toggle de cifrado E2E), unirse por id, lista de rooms.
- Centro: mensajes en vivo por SSE, burbujas con autor y hora, composer.
- Lateral: miembros (rol owner), invitar por peer conectado, expulsar (owner).
- Mantine v9 (createTheme + MantineProvider), @tabler/icons-react, layout con
  AppShell/Stack/Group; sin Tailwind ni CSS manual. React 19 (peer dep de v9).

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

web/src/App.tsx

@@ -0,0 +1,29 @@
+import { useState } from "react";
+import { GatewayClient } from "./api";
+import type { Peer } from "./types";
+import { ConnectScreen } from "./components/ConnectScreen";
+import { ChatLayout } from "./components/ChatLayout";
+
+// Connection holds the live gateway client plus the identity it connected as.
+interface Connection {
+  client: GatewayClient;
+  peer: Peer;
+}
+
+// App is the root: it shows the connect screen until the user picks a gateway
+// URL and a peer name, then swaps to the full chat layout. Disconnecting drops
+// back to the connect screen.
+export function App() {
+  const [conn, setConn] = useState<Connection | null>(null);
+
+  if (!conn) {
+    return <ConnectScreen onConnect={(client, peer) => setConn({ client, peer })} />;
+  }
+  return (
+    <ChatLayout
+      client={conn.client}
+      peer={conn.peer}
+      onDisconnect={() => setConn(null)}
+    />
+  );
+}