How can I sort results by contextual filter value?

To accomplish this, you need to alter the views query with hook_views_query_alter in your custom module. Read out the requested URL and get the related taxonomy term to it. Then you can adjust the query according to your needs. A similar answer can be found here: How to sort on different columns in the same view?

Here is an example:

use Drupal\views\Plugin\views\query\QueryPluginBase;
use Drupal\views\ViewExecutable;

function MYMODULE_views_query_alter(ViewExecutable $view, QueryPluginBase $query) {
  // Determine view by id and current display.
  if ($view->id() == 'content_recent' && $view->current_display == 'default') {
    // Get the requested path.
    $request = \Drupal::request();
    $path = $request->getPathInfo();

    // Use some logic to get the term for the current path.
    // @see https://drupal.stackexchange.com/a/266084/15055
    $tid = FALSE;
    if ($path == 'example') {
      $tid = 9;
    }

    // If the URL belongs to a term, we change the order.
    if ($tid) {
      // You may need to add a relationship to the taxonomy terms,
      // if your view is not already doing this or add it in the Views UI.

      $sql = "CASE
        WHEN taxonomy_term_field_data_node_field_data.tid = $tid THEN 0
        ELSE 1
      END";
      // Add the sql formula for sorting.
      $query->addField(NULL, $sql, 'related_taxonomy_term');
      // We first sort by the related term and than by the views settings,
      // which should for example be the changed date descending.
      $query->orderby = array_merge([[
        'field' => 'related_taxonomy_term',
        'direction' => 'ASC',
      ]], $query->orderby);
    }
  }
}