How to write a template_preprocess_node hook to get the Image Style for an Image field?
It is part of the render array generated by the formatter: https://api.drupal.org/api/drupal/core%21modules%21image%21src%21Plugin%21Field%21FieldFormatter%21ImageFormatter.php/function/ImageFormatter%3A%3AviewElements/8.2.x

You can see that it is set on #image_style, so in node preprocess, that should be $variables['content'][field_imge][0]['#image_style'].

Depending on what you want to do, you could also write your own formatter or you could preprocess/alter the image_formatter template.