If I store each of my automations in a folder under config, as separate files, should I have visibility to them through the UI? Or, how can I have visibility to them through the UI?
Yes, you can see them in the UI (with the current HA version anyway), you see the following message when you try to edit it:
This automation can not be edited from the UI, because it is not stored in the automations.yaml file, or doesn’t have an ID.