Append a code when at the current page in wp_list_pages()

Question

I would use a custom walker and then extend the Walker_Page::start_el() method, like so:

// Based on Walker_Page for WordPress v6.0
// @link https://github.com/WordPress/wordpress-develop/blob/6.0/src/wp-includes/class-walker-page.php#L105-L219

class My_Walker_Page extends Walker_Page {
    public function start_el( &$output, $data_object, $depth = 0, $args = array(), $current_object_id = 0 ) {
        /* This checks if the current page in the list is the current page you're on.
         * - $current_object_id is the ID of the current page you're on
         * - $data_object->ID is the ID of the current page in the list
         */
        $is_current_page = ( (int) $current_object_id === (int) $data_object->ID );

        // This one adds the "read more" inside the link, i.e. before the </a> tag.
        if ( $is_current_page ) {
            $args['link_after'] .= ' READ MORE 1 (inside "a")';
        }

        // Call the parent method to build the (complete) <li ...><a ...>...</a> part.
        parent::start_el( $output, $data_object, $depth, $args, $current_object_id );

        // This one adds the "read more" outside the link, i.e. after the </a> tag,
        // but still inside the same or current LI element.
        if ( $is_current_page ) {
            $output .= ' READ MORE 2 (outside "a")';
        }
    }
}

Things to note:

You could instead use a conditional tag such as is_page( $data_object->ID ) or is_single( $data_object->ID ), but using the above (int) $current_object_id === (int) $data_object->ID is easier because it works regardless the post type.
Just choose one of the if ( $is_current_page ) { ... } blocks above, or use both if you want to.. 🙂

And then pass an instance of the above class to wp_list_pages() (via the walker argument), e.g.

// NOTE: It's up to you on how to load the PHP FILE which defines the My_Walker_Page
// class, but for example, require_once __DIR__ . '/includes/class-my-walker-page.php';

wp_list_pages( array(
    'walker' => new My_Walker_Page(),
) );

Additional Notes

Your dkc_list_subpgm() code could be simplified like so where I used just one wp_list_pages() instead of two:

function dkc_list_subpgm() {

    global $post;

    $child_of = $post->ID;
    if ( is_singular( 'pgm' ) && $post->post_parent ) {
        $child_of = $post->post_parent;
    }

    $childpages = wp_list_pages( array(
        'post_type'   => 'pgm',
        'sort_column' => 'menu_order',
        'title_li'    => '',
        'child_of'    => $child_of,
        'echo'        => 0, // just use 0 (without quotes) and not '0'
        'walker'      => new My_Walker_Page(),
    ) );

    if ( $childpages ) {
        return '<ul class="wpb_page_list">' . $childpages . '</ul>';
    }

    return '';

}

Additional Notes

Related Posts: