Why is my twig variable not working inside my block twig?
Because the field is being rendered, which is different than evaluating its value. content.field_content_side is a render array which holds a lot more than just 'value'.

Try:

{% if node.field_content_side.value == 'left' %}


To get this in a block, you would add this to mytheme.theme:

/**
 * Implements hook_preprocess_block().
 * @param $variables
 */
function mytheme_preprocess_block(&amp;$variables) {
  if (isset($variables['elements']['content']['#block_content'])) {
    $variables['block_content'] = $variables['elements']['content']['#block_content'];
  }
}


Then:

{% if block_content.field_content_side.value == 'left' %}