Hello Qin, Jiang,
Apologies for the delay in my response.
If you intend to use the private for the azure backup vault, Currently, private endpoints are not supported for Backup vaults.
please refer to the below doc.
https://learn.microsoft.com/en-us/azure/backup/private-endpoints-overview#before-you-start
Hence, If you're planning to use private endpoints for secure backup traffic, you'll need to use a Recovery Services vault and ensure it's set up before any backup items are registered.
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Thanks