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>

src/components/pwa-register.tsx

@@ -0,0 +1,28 @@
+"use client";
+
+import { useEffect } from "react";
+
+export function PwaRegister() {
+  useEffect(() => {
+    if (!("serviceWorker" in navigator)) return;
+
+    navigator.serviceWorker
+      .register("/sw.js", { scope: "/" })
+      .then((reg) => {
+        reg.addEventListener("updatefound", () => {
+          const next = reg.installing;
+          if (!next) return;
+          next.addEventListener("statechange", () => {
+            if (next.state === "installed" && navigator.serviceWorker.controller) {
+              // New version available — the next navigation will pick it up
+              // because skipWaiting() is called in the SW install handler.
+              console.info("[famapp] Service worker updated.");
+            }
+          });
+        });
+      })
+      .catch((err) => console.warn("[famapp] SW registration failed:", err));
+  }, []);
+
+  return null;
+}