Phase 1: auth, room CRUD, WebSocket chat, PWA frontend

Invite-only FastAPI + SQLAlchemy(async) + Postgres backend (session-cookie
auth via CLI-provisioned accounts, open-room CRUD, single-instance /ws/chat)
and a React + Vite PWA frontend (login, room list, chat view). Backend tests
pass against a local Postgres DB. See README.md and backend/README.md for
setup, and ARCHITECTURE.md for the full phased design.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

frontend/src/main.tsx

@@ -0,0 +1,13 @@
+import { StrictMode } from 'react'
+import { createRoot } from 'react-dom/client'
+import { BrowserRouter } from 'react-router-dom'
+import './index.css'
+import App from './App.tsx'
+
+createRoot(document.getElementById('root')!).render(
+  <StrictMode>
+    <BrowserRouter>
+      <App />
+    </BrowserRouter>
+  </StrictMode>,
+)