For example, if I want to set up a suppression list that I want to be able to give mailers a URL to in order to download, I would need to get the list from the mailwizz system through API.
To download the subscribers from a certain list you mean?
If so, you'd want to use last link and loop through all subs and download them and write them in a file.
The API is really designed for developers with a sense of adventure