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Based on the details provided there are possible root causes, resolutions and questions that I would like to share is-
• If you are encountering issues with private endpoint connection, it is recommended to approve the private endpoint connection on the Azure SQL Database. You can navigate to the Networking page under Security and select the Private access tab to perform this action.
•Regarding the storage account firewalls, adding IP ranges to the network list may not be helpful for Database Export/Import operations. Instead, it is advised to allow all networks in the storage account firewalls.
• If you are still experiencing difficulties with the export, you can consider using SSMS or sqlpackage.exe to perform the export operations from your local machine. The relevant document provides a link to the documentation that explains how to export to a BACPAC file using the sqlpackage utility. - Export a database to a BACPAC file - Azure SQL Database & Azure SQL Managed Instance | Microsoft Learn
Thank You!