Why does it read “last sync: none” even if the files are already synced?

It means that the sync was never completed successfully. It may look like all files are already synced, but some files may be missing or synced incorrectly. On the side of the sync item you should see a button with the error count: clicking on it will show all the errors that happened during the last sync. For more information, see Sync errors.

When a sync completes without errors, the last sync date is updated accordingly.