Replacement for _drush_file_private_path()
_drush_file_private_path()
_drush_file_public_path()

in the end were just wrapper functions of

\Drupal\Core\StreamWrapper\PrivateStream::basePath()
\Drupal\Core\StreamWrapper\PublicStream::basePath()

And you probably get the same from

\Drupal::service('file_system')-&gt;realpath('private://')
\Drupal::service('file_system')-&gt;realpath('public://')