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>

package.json

@@ -20,7 +20,8 @@
     "db:generate": "drizzle-kit generate",
     "db:migrate": "drizzle-kit migrate",
     "db:seed": "tsx --env-file=.env scripts/seed.ts",
-    "db:studio": "drizzle-kit studio"
+    "db:studio": "drizzle-kit studio",
+    "gen:icons": "node scripts/generate-icons.mjs"
   },
   "devDependencies": {
     "@eslint/eslintrc": "^3.3.5",