How does new music gets added to my external drive? Should I add it in Serato DJ first and then sync it? Or the idea is that I get cloud storage to keep the library stored like that?

The watch folder auto-imports tracks added to a specific folder, like your Downloads folder:
https://www.mixo.dj/guides/watch-folder

In the next release (I'm working on some improvements), when Move&Rename is active and you add tracks to your Watch Folder, MIXO will import the tracks then move them to the new location.

You can optionally delete them from the Watch Folder afterwards, using the Move&Rename settings. They will visually remain in the watch Folder in MIXO, because it acts as a playlist, but the tracks will be removed from the actual system folder. You can empty the watch folder or right-click the tracks and remove them, just like with a playlist.