Hi,
Yes, there are write transaction costs in addition to the data storage fee. Depending on your storage account and what features you are using, there are several other charges that may be applicable as well. One example, if your account is GRS, RA-GRS, GZRS, or RA-GZRS you would have data transfer charges for replicating to the paired Azure region.
Please article below for details of blob storage pricing:
https://azure.microsoft.com/en-us/pricing/details/storage/blobs/
What I would recommend is to test by copying a small (say, several hundred GiB) representative subset, waiting at least 72 hours, and then going to Cost Management - Cost analysis (preview) in Azure portal to examine costs for the period involved.
Please click Accept Answer if the above was helpful.
Thanks.
-TP