Hi @lilrkt,
There’s no actual “public/private” property on a task object. From a data model standpoint, a public task is simply a task that is not assigned to any projects or teams, and thus is accessible to the entire organization. If you just create a task and don’t assign it to any projects, by definition it’ll be a public task.
You can see a little more about this topic here:
(FYI I moved your post to the “Developers & API” forum section since, while I know it mentions Zapier, it’s more of an API question.)