Add background sync runner and rejected-sync UX

lib/features/sync/sync_auto_trigger_controller.dart

@@ -0,0 +1,53 @@
+import 'package:flutter/foundation.dart';
+import 'package:relationship_saver/features/sync/sync_coordinator.dart';
+
+typedef SyncNowRunner = Future<SyncRunResult> Function();
+
+/// Coordinates auto-triggered sync calls with cooldown and concurrency guards.
+class SyncAutoTriggerController {
+  SyncAutoTriggerController({
+    required SyncNowRunner syncNow,
+    required DateTime Function() now,
+    this.minimumInterval = const Duration(minutes: 3),
+  }) : _syncNow = syncNow,
+       _now = now;
+
+  final SyncNowRunner _syncNow;
+  final DateTime Function() _now;
+  final Duration minimumInterval;
+
+  bool _running = false;
+  DateTime? _lastTriggeredAt;
+
+  @visibleForTesting
+  bool get isRunning => _running;
+
+  @visibleForTesting
+  DateTime? get lastTriggeredAt => _lastTriggeredAt;
+
+  /// Triggers `syncNow` when not already running and outside cooldown window.
+  Future<bool> trigger({bool ignoreCooldown = false}) async {
+    if (_running) {
+      return false;
+    }
+
+    final DateTime now = _now();
+    final DateTime? last = _lastTriggeredAt;
+    if (!ignoreCooldown &&
+        last != null &&
+        now.difference(last) < minimumInterval) {
+      return false;
+    }
+
+    _running = true;
+    _lastTriggeredAt = now;
+    try {
+      await _syncNow();
+      return true;
+    } catch (_) {
+      return true;
+    } finally {
+      _running = false;
+    }
+  }
+}