Implement PWA shell (task 50)

Add web manifest, placeholder icons, app-shell service worker, and
install prompt so famapp is installable on iOS and Android home screens.

- public/manifest.webmanifest — name, short_name, standalone display,
  start_url /, all four icon sizes (192/384/512 + maskable)
- public/icon-{180,192,384,512,512-maskable}.png — indigo placeholder
  squares generated by scripts/generate-icons.mjs (pnpm gen:icons)
- public/icon.svg — house-icon SVG source for future branded export
- public/sw.js — hand-rolled app-shell SW: precaches offline.html,
  cache-first for /_next/static/, network-first navigation with offline
  fallback, network-only for /api/*
- public/offline.html — branded offline fallback page
- src/components/pwa-register.tsx — client SW registration
- src/components/install-prompt.tsx — dismissible install banner:
  beforeinstallprompt on Android, "Add to Home Screen" hint on iOS
- Root layout: viewport themeColor, manifest/appleWebApp metadata,
  apple-touch-icon, mounts PwaRegister + InstallPrompt

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

public/icon.svg

@@ -0,0 +1,12 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" width="512" height="512">
+  <!-- Background -->
+  <rect width="512" height="512" rx="80" fill="#4F46E5"/>
+  <!-- House body -->
+  <polygon points="256,108 396,234 364,234 364,392 148,392 148,234 116,234" fill="white"/>
+  <!-- Door -->
+  <rect x="212" y="296" width="88" height="96" rx="6" fill="#4F46E5"/>
+  <!-- Left window -->
+  <rect x="164" y="254" width="66" height="54" rx="6" fill="#4F46E5" opacity="0.55"/>
+  <!-- Right window -->
+  <rect x="282" y="254" width="66" height="54" rx="6" fill="#4F46E5" opacity="0.55"/>
+</svg>