Hierarchical taxonomy list with modificated term links

This can be achieved multiple ways. One of them is to filter term link with your desired structure.

Following is a function that can convert a term link as per your structure. Ignore the first argument, it is there as we will be using this function as a filter callback.

/**
 * @param string  $termlink Term link.
 * @param WP_Term $term Term object.
 */
function wpse366737_pre_term_link( $termlink, $term ) {
    return add_query_arg(
        'fwp_typ', 
        FWP()->helper->safe_value( $term->slug ), 
       'https://www.MYWEBSITE.com/'
    );
}

Now, we have a function that we can use at appropriate place to modify term link. Once we are done, we will remove the filter so that other scripts using term link does not gets affected.

global $post;

$taxonomy = 'MY_TAXONOMY';

$terms = wp_get_post_terms( $post->ID, $taxonomy, array( "fields" => "ids" ) );

if ( $terms ) {
    echo '<ul>';

    $terms = trim( implode( ',', (array) $terms ), ' ,' );

    // as we needed.
    add_filter( 'pre_term_link', 'wpse366737_pre_term_link', 10, 2 );

    // this list will display the filtered url for term.
    wp_list_categories( 'title_li=&taxonomy=' . $taxonomy . '&include=" . $terms );

    // remove the filter so other script doesn"t get affected.
    remove_filter( 'pre_term_link', 'wpse366737_pre_term_link', 10 );

    echo '</ul>';
}