Adding files to the folders is quite cumbersome. Don't do it.
You probably won't like the solution but why not have a SharePoint Site with your templates unzipped?
You can copy the folder to the destination (empty folders and all). If the folders are empty, you won't gain much in zipping them anyway.
Here are the steps (I have a full article with all details here)
1. Create the SharePoint site with the templates

2. Create a Simple Flow
I'm using the same instance as source and destination for this example.

3. Run the flow


Let me know if this solves your issue and don't forget to mark as "Accepted" if this helped.