Deployment using Composer replacing old style install but issues with legacy Drush
As @Jaypan commented, globally you only need the Drush Launcher as phar file. And remove the old globally installed Drush version, this install method via composer global require is no longer supported. If you still need a legacy Drush version for other Drupal sites, download it the same way as phar file, see http://docs.drush.org/en/8.x/install. Which then can act as launcher by the way, so you don't need the Drush Launcher in this case.