How to render a media entity image (that uses a focal point image style) inside a paragraph twig file?
You'll run into troubles with this technique, because Media images are entities on their own, and have their own cache settings. So if you change the image style on paragraph level, the embedded media image will not know anything of this and instead returns the first, cached size.

Instead create multiple display view modes for your media entities, and let your editors choose the view mode on paragraph level. Below is the code I'm using in my own projects

function wtfrontend_base_preprocess_paragraph__image(array &amp;$variables) {
  $paragraph = $variables['paragraph'];

  if ($paragraph-&gt;hasField('field_image_viewmode_image')) {
    $imageViewMode =  $paragraph-&gt;field_image_viewmode_image-&gt;value;
    if (isset($variables['content']['field_image']['0']['#view_mode'])) {
      $variables['content']['field_image']['0']['#view_mode'] = $imageViewMode; 
      unset($variables['content']['field_image']['0']['#cache']['keys']);
    }
  }
}


Render the image normally with {{ content.field_image }}