@Tom Nijhof Thanks for reaching out to Microsoft Q&A.
Can you confirm how you are moving the storage account from one tenant to another?
As you mentioned, moving an account would result in writing Blobs to the new account for every Blob which means write operations for every Blob by the application/tool/API that is copying the Blobs.
Does that answer your question? Please let me know if you have any further questions/concerns. Thank you!