However, once I extract the zips (or download the dataset through Python API or CLI) not all the files are there.

and all the files are registered in the metadata? coulf you add --verbose to the sync command to see what it is doing

"clearml-data add --folder ./*" seems to fix this issue though it doesn't preserve my directory structure

This is also odd, it should Not flatten the folder structure. What is your OS / Python / clearml version?
Is this reproducible ? if so, how could we reproduce and debug?