There are a few ways to skin this cat. While the keys for Captcha are added in Kentico settings, you will then need to build captcha into your Kentico 13 site. While you might be tempted to just add the scripts to the pages, I'd recommend building a view component for recaptcha that pulls the settings keys, and adding the component to the views as needed for login and password reset.
https://learn.microsoft.com/en-us/aspnet/core/mvc/views/view-components?view=aspnetcore-9.0