I think you’re not the first person to think that CloudKit is Apple’s sync system. It doesn’t save anything visibly to your iCloud Drive (I.e. you’re not essentially copying a set of files to your iCloud folders).
It’s far clearer to consider these as 2 entirely separate systems. Your iCloud drive is a set of folders whose content you control. CloudKit is a tool Apple makes available to sync things across different devices.
P.s. you also wouldn’t want to sync your DT database with another app. DT’s folder structure is a little quirky and the groups you’ve set up on DT wouldn’t translate to the same groups/folders in another app.