Fixing json property name to match with the settings file (#28189)

src/settings-ui/Settings.UI.Library/FileLocksmithLocalProperties.cs

@@ -3,6 +3,7 @@
 // See the LICENSE file in the project root for more information.
 
 using System.Text.Json;
+using System.Text.Json.Serialization;
 using Microsoft.PowerToys.Settings.UI.Library.Interfaces;
 
 namespace Microsoft.PowerToys.Settings.UI.Library
@@ -14,6 +15,7 @@ namespace Microsoft.PowerToys.Settings.UI.Library
             ExtendedContextMenuOnly = false;
         }
 
+        [JsonPropertyName("showInExtendedContextMenu")]
         public bool ExtendedContextMenuOnly { get; set; }
 
         public string ToJsonString()