I'm building a function for my WordPress plugin that will display a dropdown list of all available pages. When I click "Save Changes" the values ​​are saved in the database perfectly. It also updates the value perfectly. However, the selected value is not displayed in the dropdown list. When "Save Changes" is clicked, the values ​​are saved, but the dropdown is reset to "Select One" again. It cannot display the selected option. Am I doing something wrong here? Any guidance would be greatly appreciated.

<form method=post>
<div class="header-right">
  <?php
  $posts = get_pages(
    array(
        'post_status' => 'publish',
    )
  );
  
  ?>
  <select name="page_for_logged_in" id="page_for_logged_in">
    <option selected="selected">选择一个</option>
    <?php
    foreach ( $posts as $page ) {
        ?>
        <option value="<?php echo esc_attr( $page->post_name ); ?>" <?php selected(get_option('page_for_logged_in'), 'page')?>><?php echo esc_html( $page->post_title ); ?></option>
        <?php
    }
    ?>
  </select>

  <?php
  if(empty($_POST['page_for_logged_in'])) {
      
    } else {
      $myvalue=$_POST['page_for_logged_in'];
      update_option('page_for_logged_in', $myvalue, $autoload = 'no');
    }
    ?>

<?php submit_button(); ?>

</p>
</br>
</br>
</form>