Hi,
Thank you for the details!
I tried to log-in to check the issue, but the details does not work, either the username or password are invalid.
I’m afraid this is not possible unfortunately. The message comes from the elementor core itself. The regular posts or product widget does not have a no-results message, so the plugin uses a hook to override that, but for the archive widget it won’t work.
I’m not sure if there is a simple way to display a custom post there either, as that works differently from the WordPress WP_Query, it uses a separate class and different hooks for that. There is this documentation, but ti does not work with the posts archive as far as I know, only the posts widget.