Where can I find CURL examples of how to communicate with the NC 11 API

I have an external website that needs to authenticate via NC 11. I want it to authenticate the user with the current NC credentials if they are not logged in. Alternately, if they are already in NC, it shows up as an “external site” which shoudl reuse the existing credentials already supplied. (Standalone site as well as NC subsite). The user should have access to specific NC files that have been shared with him or her. If said file is accessible, the user is allowed to see the site. If the said file is not accessible, the user is not allowed to see the site.

The reason for this is that external users may be given special NC accounts, but we do not want to have them see the NC banner when they come in externally. When our regular team logs in, they can see the banner if used from w/in NC. This is a matter of screen real-estate and not preference.

The issue I am facing is that I am not able to locate documentation on how to do so. Specifically, I see a lot of discussion on “how this and that API might work” for the External API once an app is created, but I see no direct CURL examples of actually authenticating against NC11 for just accessing existing files. (E.g. the app already exists - it is the main files app).

Can someone please direct me to the correct page where I can learn how to do this? I already have the old framework from the OC7.0.1.1 days, but those days of directly logging in will no longer work.

Also, can the External API handle login via Google Authenticator?