There is an AppStore app, I am not sure if this is the one we are talking about? <https://github.com/GrapheneOS/AppStore/blob/main/app/src/mai...>

That one lists:

  ACCESS_NETWORK_STATE
  ENFORCE_UPDATE_OWNERSHIP
  FOREGROUND_SERVICE
  FOREGROUND_SERVICE_SPECIAL_USE
  INSTALL_PACKAGES
  INTERNET
  POST_NOTIFICATIONS
  QUERY_ALL_PACKAGES
  RECEIVE_BOOT_COMPLETED
  REQUEST_DELETE_PACKAGES
  REQUEST_INSTALL_PACKAGES
  UPDATE_PACKAGES_WITHOUT_USER_ACTION

That's grapheneos's own app, separate from the play store or play services.