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/manifest.webmanifest

@@ -0,0 +1,32 @@
+{
+  "name": "famapp",
+  "short_name": "famapp",
+  "description": "Family coordination app",
+  "start_url": "/",
+  "display": "standalone",
+  "background_color": "#ffffff",
+  "theme_color": "#4F46E5",
+  "icons": [
+    {
+      "src": "/icon-192.png",
+      "sizes": "192x192",
+      "type": "image/png"
+    },
+    {
+      "src": "/icon-384.png",
+      "sizes": "384x384",
+      "type": "image/png"
+    },
+    {
+      "src": "/icon-512.png",
+      "sizes": "512x512",
+      "type": "image/png"
+    },
+    {
+      "src": "/icon-512-maskable.png",
+      "sizes": "512x512",
+      "type": "image/png",
+      "purpose": "maskable"
+    }
+  ]
+}