//services/identity/public/cpp contains the next-generation C++ API for interacting with the user's Google identities. In the long term, this library will become a client library for the Identity Service. In the present, it is being developed based directly on the internal C++ classes in //components/signin and //google_apis/gaia. This library is almost certainly what you want to use if you are developing a browser feature. See //services/identity/public/cpp/README.md for details.
If you are looking to connect to the Identity Service, the current way to do so is via //services/identity/public/mojom. You may wish to do this if you are developing a feature that is intended to run out of the browser process and does not require having a view of Google identity that is synchronously updated with the view of Google identity that the browser sees.