This is just a 3rd party service (not affiliated with HN) checking peoples HN profiles (which are public) for a unique string that the 3rd party service asks said user to set. It's a bit like how custom domains names are added to (for example) GSuite email.

As an application developer, you get no access to HN because the 3rd party service doesn't have any access to HN to begin with. It's all just a clever workaround to validate "ownership" of a HN profile.