You can download files and folders from Azure File storage using this PowerShell script. You can use service principal who has access to Key vault and storage account. The storage account secret can be saved in Key vault to be accessed through PowerShell script.
Service Principal can be authenticated for azure resources by adding scripts to Pre-Request Scripts section in Postman.
REST API for the Blob service can be used to upload, manage, organize, and delete text and binary data.
Postman can make REST API call to get access_token for a service principal authenticated with Azure AD.
Storage Account RestAPI PUT call can be used to create storage account using Postman