SetDesk — control-plane
  ws   /rooms/<name>/connect[?role=operator|guest|supervisor][&hint=<region>]
  GET  /rooms/<name>/state
  POST /auth/sign-up/email | /auth/sign-in/email    {email, password}
  GET  /me                                          (session required)
  POST /broadcasts                 {roomId, region, destinations[]}  (session required)
  GET  /broadcasts/<id>/state                                        (owner only)
  POST /broadcasts/<id>/stop                                         (owner only)