It's easy to get a list of taxonomy. wp_get_post_terms, get_term_list,..do the job. However, in the case you don't know the taxonomy name, then here is the code to find out it. This is take from WordPress core file. Meaning the function we need is: get_object_taxonomies

Get object taxonomy of a custom post type.php

<?php
 
function get_post_taxonomies($post) {
// Passing an object
// Why another var?? $output = 'objects'; // name / objects
$taxonomies = get_object_taxonomies($post, 'objects');
 
/*// Passing a string using get_post_type: return (string) post, page, custom...
$post_type = get_post_type($post);
$taxonomies = get_object_taxonomies($post_type, 'objects');*/
 
/*// In the loop with the ID
$theID = get_the_ID();
$post_type = get_post_type($theID);
$taxonomies = get_object_taxonomies($post_type, 'objects');*/
 
// You can also use the global $post
 
// edited to fix previous error $tazonomies
// edited to force type hinting array
return (array) $taxonomies; // returning array of taxonomies
}