Proof-of-concept for a shortcode taxonomy.

gistfile1.php

<?php
function eam_register_taxonomy() {
	$labels = array(
		'name'              => _x( 'Shortcodes', 'taxonomy general name' ),
		'singular_name'     => _x( 'Shortcode', 'taxonomy singular name' ),
		'search_items'      => __( 'Search Shortcodes' ),
		'all_items'         => __( 'All Shortcodes' ),
		'parent_item'       => __( 'Parent Shortcode' ),
		'parent_item_colon' => __( 'Parent Shortcode:' ),
		'edit_item'         => __( 'Edit Shortcode' ),
		'update_item'       => __( 'Update Shortcode' ),
		'add_new_item'      => __( 'Add New Shortcode' ),
		'new_item_name'     => __( 'New Shortcode Name' ),
		'menu_name'         => __( 'Shortcode' ),
	);

	$args = array(
		'hierarchical'      => false,
		'labels'            => $labels,
		'show_ui'           => false,
		'show_admin_column' => false,
		'query_var'         => false,
		'rewrite'           => false,
	);

	register_taxonomy( 'eam_shortcode', array( 'post' ), $args );
}
add_action( 'init', 'eam_register_taxonomy' );

function eam_save_shortcodes( $post_id, $post ) {
	global $shortcode_tags;
    
	if ( 'post' !== $post->post_type ) {
		return;
	}

	if ( defined( 'DOING_AUTOSAVE' ) && DOING_AUTOSAVE ) {
		return;
	}

	$shortcodes = array_keys( $shortcodes_tags );
	$to_set = array();
	$to_remove = array();

	foreach( $shortcodes as $shortcode ) {
		if ( has_shortcode( $post->post_content, $shortcode ) ) {
			$to_set[] = $shortcode;
		} else {
			$to_remove[] = $shortcode;
		}   
	}

	wp_add_object_terms( $post_id, $to_set, 'eam_shortcode' );
	wp_remove_object_terms( $post_id, $to_remove, 'eam_shortcode' );
}
add_action( 'save_post', 'eam_save_shortcodes', 10, 2 );