Get current post's nav menu name (term name)

Question

I want to get the nav menu name by the current post ID. After hours searching in my database I found out that navigation menus are basically just terms of the taxonomy 'nav_menu'. But for some reason they don't work the same.

I have tried to get the terms (nav menu's) with the get_the_terms() function, but this does not return anything.

global $post;
get_the_terms( $post->ID, 'nav_menu' );

I cannot find another function to get the 'terms' of the 'nav_menu' taxonomy. wp_get_nav_menu_items for example, returns the posts in the menu, and that is not what I need.

I think I need to make my own function, but I cannot find how the database structure for navigation menus work..

EDIT:

I made the following function which works, But @Rars showed me a quicker and cleaner option.

function get_post_menu( $post_id = null, $output = 'term_id' ) {
    if( ! isset( $post_id ) ) {
        global $post;
        $post_id = $post->ID;   
    }
    global $wpdb;
    $menu = $wpdb->get_results( "
        SELECT term_taxonomy_id 
        FROM $wpdb->term_relationships
        WHERE object_id = 
        (SELECT post_id 
        FROM $wpdb->postmeta 
        WHERE meta_key = '_menu_item_object_id' 
        AND meta_value = $post_id)"
        , OBJECT 
    );
    $term = get_term_by( 'term_taxonomy_id', $menu[0]->term_taxonomy_id, 'nav_menu' );
    return $term->$output;
}

Answer 1

You are missing a link. The posts are not assigned to the menus directly. There is a post type nav_menu_item in nav_menu taxonomy which links posts (or other kinds of destinations) to their place in menu.

This snippet should get you started on retrieval:

$menu_items = get_posts( [
    'post_type'  => 'nav_menu_item',
    'meta_query' => [
        [
            'key'   => '_menu_item_object_id',
            'value' => get_the_ID(),
        ]
    ],
] );

foreach ( $menu_items as $menu_item ) {
    var_dump( get_the_terms( $menu_item->ID, 'nav_menu' ) );
}