WordPress 的 publish_post 钩子针对的是文章（帖子）类型，适用于 WordPress 站点的 post 类型的文章。如果想要发布页面时执行某些动作，对应钩子应该是 publish_page；如果你想发布某个自定义类型的文章，如课程类型course，那么对应钩子应该是 publish_course。针对你上面的代码，你可以如下修改：

//发布文章或提问奖励声望
function publish_article_prestige( $post_ID ){
    global $wpdb; 
    $user_id = get_post($post_ID)->post_author; 
    $old_pretige = get_user_meta( $user_id,"shengwang",true);
    $apply_pretige = 5;
    $post_cat = get_the_category($post_ID)[0]->cat_ID;
    if($post_cat == 2){
      $publish_type = "publish_question";
    } else {
      $publish_type = "publish_post";
    }
    $date = date('Y-m-d H:i:s');
    $new_pretige = $old_pretige+$apply_pretige;
    $wpdb->insert('wp_prestige_log', array(
        'user_id' => $user_id,
        'post_id' => $post_ID,
        'old' => $old_pretige, 
        'apply' => $apply_pretige, 
        'new' => $new_pretige, 
        'type' => $publish_type, 
        'time' => $date, 
    ));
   update_user_meta($user_id,'shengwang',$new_pretige);
}
add_action('publish_post','publish_article_prestige');

//发布课程（自定义文章类型）奖励声望
function publish_course_prestige( $post_ID ){
    global $wpdb; 
    $post_type = get_post_type( $post_ID );
    $user_id = get_post($post_ID)->post_author; 
    $old_pretige = get_user_meta( $user_id,"shengwang",true);
    $apply_pretige = 10;
    $publish_type = "publish_course";
    $date = date('Y-m-d H:i:s');
    $new_pretige = $old_pretige+$apply_pretige;
    $wpdb->insert('wp_prestige_log', array(
        'user_id' => $user_id,
        'post_id' => $post_ID,
        'old' => $old_pretige, 
        'apply' => $apply_pretige, 
        'new' => $new_pretige, 
        'type' => $publish_type, 
        'time' => $date, 
    ));
   update_user_meta($user_id,'shengwang',$new_pretige);
}
add_action('publish_course','publish_course_prestige');