Google Captcha is hidden upon calculating the shipping cost in Drupal Commerce checkout form

In Drupal, when a form is rebuilt due to AJAX calls (like recalculating shipping costs), any dynamically added elements need to be added again in the buildForm function or the appropriate form alter hook. Since you're using hook_form_alter, you need to make sure that the CAPTCHA is added back to the form whenever it is rebuilt. To do this, you can implement hook_form_alter and check if the form is being rebuilt during the AJAX callback.

function beyond_shipping_form_alter(&$form, FormStateInterface $form_state, $form_id) {
  if ($form_id == 'commerce_checkout_flow_multistep_default') {
    // Add CAPTCHA to the form
    $default_challenge = \Drupal::service('config.manager')
      ->getConfigFactory()
      ->get('captcha.settings')
      ->get('default_challenge');

    // Always set the CAPTCHA in the form
    $form['captcha'] = [
      '#type' => 'captcha',
      '#captcha_type' => $default_challenge,
    ];

    // Check if the form is being rebuilt during an AJAX callback
    if ($form_state->getTriggeringElement()['#ajax']) {
      // If it's an AJAX request, we can optionally add any necessary logic here
    }
  }
}