The API route doesn't render a template. It just outputs the JSON that is passed into render.
You can test this by prepending /api on any route, you'll see JSON output.
The purpose of this is for the AJAX loading of the next page.
How do I redirect
sso-* plugins after successful log in to a custom route instead of homepage
This is an old post, but have you found a solution? I have the exact same problem. I need a new user to be redirected to profile edit page to enter the email address.