On the first start with S3 enabled, all data is moved automatically from local file system to S3 (that feature is part of the blob store API). This happens the moment the blob store is accessed, so for the extension repository the moment the extension repository is accessed for the first time.
From what I understand, at many cloud providers, internal network transfer is free. The way we use object storage in XWiki, all transfer goes through XWiki, so the network transfer cost should be the same for both types of storage. At OVH, even classic block storage is 0.04307 EUR/GB/month while standard object storage is 0.0070956 EUR/GB/month, so more than a factor four cheaper. Even high-performance object storage is just 0.01825 EUR/GB/month, so still more than a factor of two cheaper than classic block storage. High-speed block storage is even twice as expensive, so if you compare the two high-performance storage types, you get a factor of four again.
In a cluster setting, storage always needs to be provided over the network due to the NFS requirement.