@Joel
Currently hosting a static website privately via blob storage is not a supported feature. After reviewing your use-case I believe you might be better suited for hosting this on Azure Static Web Apps. You can setup to restrict access to your web app so that it is only available on your private network. Review the quickstart documentation to see if this might be a suitable alternative for your application.
Hope this helps! Let us know if you have more questions and we will do our best to assist.
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