CiviCRM public theme always the same as the CiviCRM Administrator theme
When running CiviCRM 5.57.1 under Drupal 9.5.2 under IIS it seems that the public theme setting is ignored; CiviCRM just uses the theme set for CiviCRM administration. To replicate got to Manage -> Appearance and select the various themes. It doesn't appear to be browser related, I see the same with Edge, Chrome, Opera and Firefox. I don't know if it is IIS specific, but, of course, being theme related can't be replicated in the Demo environment.