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My solution to this problem when extending the Walker_Nav_Menu was to skip check if current_page_parent when C.P.T. I identified C.P.Ts following this stackexchange post.

This does not entirely solve the problem as I am using current_page_item for C.P.T parent menu items, but it does achieve the desired outcome. Here is my class.

class My_Menu extends Walker_Nav_Menu {  

  public function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 ) {
    
    $post_type = get_post_type();
    $class_names = '';

    // Check if post_type - $item->attr_title returns the WP Menu custom link Title Attribute
    $class_names .= ($item->attr_title != '' && $item->attr_title == $post_type || in_array("current_page_item", $item->classes)) ? 'current_page_item' : '';

    // Prevent Blog menu item from getting the current_page_parent class when Custom Post Type
    if(!is_post_type_archive() && !is_singular(array( 'custom-one', 'custom-two'))){
    $class_names .= in_array("current_page_parent", $item->classes) ? ' current_page_parent' : '';
    }

    $id = apply_filters( 'nav_menu_item_id', 'menu-item-'. $item->ID, $item, $args );
    $id = $id ? ' id="' . esc_attr( $id ) . '"' : '';
    $class_names = $class_names ? ' class="' . esc_attr( $class_names ) . '"' : '';

    $output .= '<li' . $id . $class_names .'>';

    $atts = array();
    $atts['title']  = ! empty( $item->attr_title ) ? $item->attr_title : '';
    $atts['target'] = ! empty( $item->target )     ? $item->target     : '';
    $atts['rel']    = ! empty( $item->xfn )        ? $item->xfn        : '';
    $atts['href']   = ! empty( $item->url )        ? $item->url        : '';

    $atts = apply_filters( 'nav_menu_link_attributes', $atts, $item, $args );

    $attributes = '';
    foreach ( $atts as $attr => $value ) {
        if ( ! empty( $value ) ) {
            $value = ( 'href' === $attr ) ? esc_url( $value ) : esc_attr( $value );
            $attributes .= ' ' . $attr . '="' . $value . '"';
        }
    }
    $item_output = $args->before;
    $item_output .= '<a'. $attributes .'>';
    $item_output .= $args->link_before . apply_filters( 'the_title', $item->title, $item->ID ) . $args->link_after;
    $item_output .= '</a>';
        
    $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args ); 
  }

  public function end_el( &$output, $item, $depth = 0, $args = array() ) {
    $output .= "</li>\n";
  }

} // Walker_Nav_Menu