PluginNotFoundException: The "node_type" plugin does not exist.

You need to update your config to use bundle:node

Thank you Lee
In my case, the configurations are being ignored, and our Drupal is used on multiple websites. Some of them might return errors after the upgrade.
I suggest manually deselecting the node bundle, before the upgrade, and selecting a different visibility solution instead. Missing doing that could cause a cross-website error.

I used a post-update function to migrate all node types to bundle:node, as Lee suggested above, to run it during the upgrade deployment process or after.

/**
 * Fix script_manager module node_type issue.
 *
 */
function ua_post_update_script_manager_node_type(){
  // Fix script manager settings.
  $config_factory = \Drupal::service('config.factory');
  $script_manager_settings = $config_factory->listAll('script_manager.settings');
  $config = $config_factory->getEditable($script_manager_settings[0]);
  $enabled_visibility_plugins = $config->get('enabled_visibility_plugins');
  if (is_array($enabled_visibility_plugins)) {
    $enabled_visibility_plugins = array_replace($enabled_visibility_plugins,
      array_fill_keys(
        array_keys($enabled_visibility_plugins, 'node_type'),
        'entity_bundle:node'
      )
    );
    $config->set('enabled_visibility_plugins', $enabled_visibility_plugins);
    $config->save();
  }
  // Fix script manager items.
  $config_factory = \Drupal::service('config.factory');
  $script_manager_configurations  = $config_factory->listAll('script_manager.script');
  foreach ($script_manager_configurations as $config_name) {
    // Load the block configuration.
    $config = $config_factory->getEditable($config_name);

    // Check for a value and update it if needed.
    if (is_array($config->get('visibility.node_type'))) {
      if ($config->get('visibility.node_type')['id'] === 'node_type') {
        $config->set('visibility.node_type.id', 'entity_bundle:node');
        $config->save();
      }
    }
  }
}