How to get total number of shortcodes in the wordpress application?

Create a new page in WordPress theme and use below code :

<?php
        global $shortcode_tags;
        echo '<pre>'; 
        print_r($shortcode_tags); 
        echo '</pre>';
?>

For details see link and another post may helps!

For specific to your requirements use below code in functions.php then use shortcode [all_shortcodes] in your page or sidebar to list shortcodes:

add_shortcode('all_shortcodes', 'all_shortcodes_display');

function all_shortcodes_display() {

  // The available shortcodes are stored in the global variable $shortcode_tags, so we need access to it
  global $shortcode_tags;

  // let's sort the list alphabetically
  $available_shortcodes = $shortcode_tags;
  ksort( $available_shortcodes );

  // show an unordered list of available shortcodes
  echo '<ul>';
  foreach ( $available_shortcodes as $key => $value ) {
    echo '<li>' . $key . '</li>';
  }
  echo '</ul>';
}

Thanks!