@Wayne Welcome to Microsoft Q&A Forum, Thank you for posting your query here!
First, it's important to note that when you're using a private endpoint, the DNS resolution should be handled by your on-premises DNS server, not the Azure DNS server. You mentioned that you have the private endpoint DNS in your AAD DS DNS server, but it's still resolving to the public IP. Have you confirmed that your on-premises DNS server is correctly configured to resolve the storage account name to the private endpoint's private IP address?
This article provides detailed information on How Connect to a storage account using an Azure Private Endpoint
Refer to this article Connect to an Azure File Share via a Private Endpoint
This article provides possible causes and solutions for errors that cause the mounting of an Azure file share to fail. It give ideas based on the error, If the issue still persist, share the screenshot of the error message.
Additional information:
Please let us know if you have any further queries. I’m happy to assist you further.
Please do not forget to "Accept the answer” and “up-vote” wherever the information provided helps you, this can be beneficial to other community members.