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/backup_section.dart

@@ -1,10 +1,12 @@
 import 'package:commons_core/commons_core.dart';
 import 'package:flutter/material.dart';
 import 'package:flutter/services.dart';
+import 'package:intl/intl.dart';
 
 import '../data/export_import/inventory_snapshot.dart';
 import '../di/injector.dart';
 import '../i18n/strings.g.dart';
+import '../services/auto_backup_service.dart';
 import '../services/export_import_service.dart';
 import '../services/recovery_sheet_service.dart';
 
@@ -15,21 +17,32 @@ import '../services/recovery_sheet_service.dart';
 /// for confirmation first (it merges into the live inventory), then reports
 /// what happened in a SnackBar.
 class BackupSection extends StatelessWidget {
-  const BackupSection({this.service, this.sheet, super.key});
+  const BackupSection({this.service, this.sheet, this.autoBackup, super.key});
 
   /// Injectable for widget tests; the app resolves them lazily (on tap) from
   /// the service locator so merely mounting Settings needs no DI setup.
   final ExportImportService? service;
   final RecoverySheetService? sheet;
 
+  /// Drives the reassurance line about automatic copies. When null (and none is
+  /// registered — e.g. web) the line is simply hidden.
+  final AutoBackupService? autoBackup;
+
   ExportImportService get _service => service ?? getIt<ExportImportService>();
   RecoverySheetService get _sheet => sheet ?? getIt<RecoverySheetService>();
 
+  AutoBackupService? get _autoBackup =>
+      autoBackup ??
+      (getIt.isRegistered<AutoBackupService>()
+          ? getIt<AutoBackupService>()
+          : null);
+
   @override
   Widget build(BuildContext context) {
     final t = context.t;
     return Column(
       children: [
+        _AutoBackupTile(service: _autoBackup),
         ListTile(
           leading: const Icon(Icons.save_alt_outlined),
           title: Text(t.backup.exportJson),
@@ -299,3 +312,37 @@ class BackupSection extends StatelessWidget {
     messenger.showSnackBar(SnackBar(content: Text(message)));
   }
 }
+
+/// A quiet reassurance line: the app already keeps copies on its own, and this
+/// says when the last one was made. Hidden entirely when there is no automatic
+/// backup on this platform.
+class _AutoBackupTile extends StatelessWidget {
+  const _AutoBackupTile({required this.service});
+
+  final AutoBackupService? service;
+
+  @override
+  Widget build(BuildContext context) {
+    final service = this.service;
+    if (service == null) return const SizedBox.shrink();
+    final t = context.t;
+    return FutureBuilder<DateTime?>(
+      future: service.lastBackupAt(),
+      builder: (context, snapshot) {
+        final last = snapshot.data;
+        final subtitle = last == null
+            ? t.backup.autoBackupNone
+            : t.backup.autoBackupLast(
+                date: DateFormat.yMMMd(
+                  LocaleSettings.currentLocale.languageCode,
+                ).format(last),
+              );
+        return ListTile(
+          leading: const Icon(Icons.shield_outlined),
+          title: Text(t.backup.autoBackupTitle),
+          subtitle: Text(subtitle),
+        );
+      },
+    );
+  }
+}