Execute remote sync if local items were pushed

lib/services/authenticator_service.dart

@@ -59,11 +59,12 @@ class AuthenticatorService {
           key,
           Sodium.base642bin(e.header),
         );
+        final hasSynced = !(e.id == null || e.shouldSync);
         entities.add(
           EntityResult(
             e.generatedID,
             utf8.decode(decryptedValue),
-            e.id != null,
+            hasSynced,
           ),
         );
       } catch (e, s) {
@@ -197,6 +198,9 @@ class AuthenticatorService {
         await _db.updateLocalEntity(entity.copyWith(shouldSync: false));
       }
     }
+    if (pendingUpdate.isNotEmpty) {
+      await _remoteToLocalSync();
+    }
   }
 
   Future<Uint8List> getOrCreateAuthDataKey() async {