Microsoft Azure Storage Explorer is a standalone app. You could access storage resources through Azure RBAC and ensure the network is connected between the on-premises network and the Azure virtual network.
As far as I know, Storage Explorer uses HTTPS by default and there is no limit to use the public Internet, you can enable the private endpoint for your Storage Account and set up the VPN connection. You also need to assign your account to access the blob, table, or other service endpoints with enough permission.
For more information:
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