Listing taxonomy phrases assigned to a publish in hierarchical view

Been attempting do that and nonetheless no luck. What I am attempting is to listing taxonomy phrases assigned to a publish ordered by parent-child class relationship (hierarchical view).

Construction is one thing like this

Library = customized publish sort      
Yr = customized taxonomy assigned to "library" 
    
- 2021 = mum or dad time period     
-- April = little one time period
-- Might = little one time period
-- June = little one time period
-- July = little one time period

The specified output is:

2021, April, Might, June, July

I attempted:

$phrases = get_the_terms( $post->ID, 'document_year' ); 
if ( $phrases && ! is_wp_error( $phrases ) ) : 
    $output = array(); 
    foreach ( $phrases as $time period ) {
        $output[] = $term->title;
    }
    echo '<span>' . implode ( ', ', $output ) . '</span>'; 
endif;

However this outputs an alphabetical order of phrases.

Identical with this:

echo ( get_the_term_list( $post->ID, 'class', '', ' / ') );

Any assist please?