@Vicente I'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this! Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I'll repost your solution in case you'd like to "Accept " the answer.
Issue: Related to the rehydration process while trying to make the copy of one blob to another account.
I have two different clients, one for the source and another for the destination. I've learned that to perform a copy to a different account, a SAS token should be used. Here's what I've done so far:
I generated a SAS token with specific permissions for the source blob. I used this token to initiate the beginCopy operation with new options for rehydration (from Archive to Cool and the priority). However, when I execute this operation, it directly creates files with a size of 0B, and there's no waiting time for the rehydrate process. This issue only occurs when copying between different accounts; copying within the same account to a different container works as expected
Solution: The reason for the issue is that my accounts were located in different regions, and the rehydrate beginCopy method is not supported for this scenario yet. You can find more information about this limitation in the documentation: https://learn.microsoft.com/en-us/azure/storage/blobs/archive-rehydrate-overview
Please remember to "Accept Answer" if any answer/reply helped, so that others in the community facing similar issues can easily find the solution.