@Maarten Munning Thanks for reaching out to Microsoft Q&A. I understand that you want to export eDiscovery to Blob storage directly.
"When you export documents from a review set in an eDiscovery (Premium) case, you have the option to export them to an Azure Storage account managed by your organization. If you use this option, the documents are uploaded to your Azure Storage location. After they are exported, you can access the documents (and download them to a local computer or other location) by using the Azure Storage Explorer. This article provides instructions for how to export documents to your Azure Storage account and the use the Azure Storage Explorer to connect to an Azure Storage location to download the exported documents. "
As per document- https://learn.microsoft.com/en-us/microsoft-365/compliance/download-export-jobs?view=o365-worldwide
You should be able to export the review set to Azure Blob Storage and then use Storage explorer and download them as needed.
I would suggest you reach out to the Tech Community for more questions regarding this here- https://techcommunity.microsoft.com/t5/forums/searchpage/tab/message?advanced=false&allow_punctuation=false&q=ediscovery
Hope this helps. Please let us know if you have any more questions and we will be glad to assist you further. Thank you!
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