Directly manipulate the field item properties

src/Plugin/Field/FieldType/BgImgItem.php

@@ -245,6 +245,6 @@ class BgImgItem extends ImageItem {
 
     // Handle the custom file extensions setting before saving.
     $extensions = preg_split('/[\s,]+/', $this->getSetting('file_extensions'));
-    $this->setSetting('file_extensions', implode(' ', array_filter($extensions)));
+    $this->file_extensions = implode(' ', array_filter($extensions));
   }
 }