Phase 3: PWA offline caching (frontend only)

Adds a real Workbox runtime-caching strategy on top of the Phase 1 app-shell
precache: StaleWhileRevalidate (cache-and-refresh) for the five read
endpoints (rooms/mine, open rooms, room messages, room members, invites/mine)
with a bounded/expiring cache per endpoint, while /api/auth/* and all
mutations stay network-only. An OfflineBanner (navigator.onLine-driven) and
a clearer Composer status line ("Connecting..." vs "You're offline") surface
what's actually happening; api/client.ts gains a NetworkError distinct from
ApiError so a genuine cache-miss-while-offline shows a quiet empty state
instead of a red error.

Manual offline testing (backend stopped, `vite preview` against the real
production service worker) surfaced a real gap the plan hadn't accounted
for: GET /api/auth/me is intentionally NetworkOnly, but that meant
ProtectedRoute could never confirm a session while offline and always
bounced to /login -- none of the newly-cached room/message data was ever
reachable. Fixed by caching a minimal, non-sensitive "last known user" in
localStorage (lib/lastUser.ts) and having AuthContext fall back to it for
any *unconfirmed* auth check (network failure, or a down backend answering
through a live reverse proxy with its own 502/503/504 -- both happen in
real deployments, not just literal airplane-mode). Only a server-confirmed
401 still clears it and signs the user out; every real action still
re-checks the actual session cookie server-side, so this can't grant
anything -- it only keeps cached UI reachable.

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

frontend/src/hooks/useOnlineStatus.ts

@@ -0,0 +1,23 @@
+import { useEffect, useState } from 'react'
+
+// navigator.onLine reflects the OS network interface, not whether our
+// backend is actually reachable -- it can be true when the API is down. This
+// is still a useful fast/cheap signal for a banner; the WebSocket
+// `connected` state (see useChatSocket) is the more reliable one for
+// whether live messaging actually works right now.
+export function useOnlineStatus(): boolean {
+  const [online, setOnline] = useState(() => navigator.onLine)
+
+  useEffect(() => {
+    const goOnline = () => setOnline(true)
+    const goOffline = () => setOnline(false)
+    window.addEventListener('online', goOnline)
+    window.addEventListener('offline', goOffline)
+    return () => {
+      window.removeEventListener('online', goOnline)
+      window.removeEventListener('offline', goOffline)
+    }
+  }, [])
+
+  return online
+}