feat(backup): add automatic weekly encrypted backups

A silent safety net against in-app data loss or DB corruption, with zero
friction. Driven off the app lifecycle (startup + when hidden), it writes a
sealed .tanemaki copy into the app's private storage once a week, keeping the
newest 3 (rotating). Reuses the manual backup's encryption via the extracted
ExportImportService.buildSealedBackup(); never throws, so a failed copy can't
crash startup or backgrounding. Not registered on web (no file storage).

Settings shows a quiet reassurance line with the date of the last automatic
copy (localised via intl), hidden where no automatic backup exists.

apps/app_seeds/lib/ui/auto_backup_gate.dart

@@ -0,0 +1,42 @@
+import 'package:flutter/widgets.dart';
+
+import '../services/auto_backup_service.dart';
+
+/// Drives the automatic backup off the app lifecycle: once on startup and again
+/// each time the app becomes hidden (backgrounded on mobile, window hidden on
+/// desktop). The [AutoBackupService] decides whether a copy is actually due, so
+/// these are cheap no-ops most of the time.
+///
+/// When [service] is null (widget tests, or platforms without file storage such
+/// as web) it wraps [child] untouched and does nothing.
+class AutoBackupGate extends StatefulWidget {
+  const AutoBackupGate({required this.child, this.service, super.key});
+
+  final Widget child;
+  final AutoBackupService? service;
+
+  @override
+  State<AutoBackupGate> createState() => _AutoBackupGateState();
+}
+
+class _AutoBackupGateState extends State<AutoBackupGate> {
+  AppLifecycleListener? _listener;
+
+  @override
+  void initState() {
+    super.initState();
+    final service = widget.service;
+    if (service == null) return;
+    _listener = AppLifecycleListener(onHide: () => service.runIfDue());
+    WidgetsBinding.instance.addPostFrameCallback((_) => service.runIfDue());
+  }
+
+  @override
+  void dispose() {
+    _listener?.dispose();
+    super.dispose();
+  }
+
+  @override
+  Widget build(BuildContext context) => widget.child;
+}