Gate auto sync with network reachability checks

test/features/sync/sync_auto_trigger_controller_test.dart

@@ -68,6 +68,11 @@ void main() {
     );
 
     final Future<bool> first = controller.trigger();
+    for (int i = 0; i < 20 && !controller.isRunning; i += 1) {
+      await Future<void>.delayed(const Duration(milliseconds: 1));
+    }
+    expect(controller.isRunning, isTrue);
+
     final bool second = await controller.trigger();
     completer.complete();
     final bool firstCompleted = await first;
@@ -76,6 +81,23 @@ void main() {
     expect(second, isFalse);
     expect(callCount, 1);
   });
+
+  test('skips trigger when connectivity gate denies run', () async {
+    int callCount = 0;
+    final SyncAutoTriggerController controller = SyncAutoTriggerController(
+      syncNow: () async {
+        callCount += 1;
+        return _result(success: true);
+      },
+      now: DateTime.now,
+      canTrigger: () async => false,
+      minimumInterval: Duration.zero,
+    );
+
+    final bool executed = await controller.trigger();
+    expect(executed, isFalse);
+    expect(callCount, 0);
+  });
 }
 
 SyncRunResult _result({required bool success}) {