@tylers-8644 Welcome to Microsoft Q&A forums.
Since the data you are moving is extremely sensitive in nature, you will need to protect it not just from unauthorized access but also from corruption and data loss.
We have documented the recommendations for securing Blob storage here - Security recommendations for Blob storage
There is also a module on Microsoft Learn that will help you understand the security and advanced threat protection features - Secure your Azure Storage account
Please go through these and let us know if you have any further questions.
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