@dmondou
If you wish to copy the data you will need either Storage Blob Data Contributor or Storage Blob Data Owner assigned to the user. Please see Use Azure Active Directory on the AzCopy page for more details.
As this issue is related to Release Pipeline I also suggest you post your issue on the dedicated DevOps forum. They should be able to better assist you in the specific configuration needed.
Hope this helps. Let us know if you have further issues or questions and we will be happy to assist.
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