I may be misunderstanding you or doing something wrong, but I've just created a new Azure Blob Storage Dataset (selecting the XML format), and I've also created a new Azure Blob Storage Linked Service for the Dataset to connect through. However, the new Dataset isn't available to select as a Sink for the Copy activity.
The following article states that the XML format "is supported as source but not sink" in ADF pipelines:
https://learn.microsoft.com/en-us/azure/data-factory/format-xml#xml-connector-behavior
Please bear in mind that I'm not trying to use ADF to shred the XML in the response to my REST API GET request. I only want to store the response "as-is", as the shredding will be performed downstream (by a stored procedure in my Azure SQL Database).