How do I automatically add a user to a Backdrop (or Drupal) role?
First, go to your modules listing and enable "CiviGroup Roles Sync":


Next, go to Drupal's Configuration menu » CiviCRM » CiviGroup Roles Sync » Add association rule:


From here, you can set the CiviCRM group that corresponds to the Backdrop/Drupal role:


Note this only works when contacts are newly added to the group (or role).  However, you can manually synchronize in the configuration settings.