R1:ab923e0a752b

Implement new reCAPTCHA interface

Summary:
Fixes T12195. For the past few years, Recaptcha (now part of Google) has supported
a new, "no captcha" one-click user interface. This new UI is stable, doesn't
require any typing or reading words, and can even work without JavaScript (if
the administrator enables it on the Recaptcha side).

Furthermore, the new Recaptcha has a completely trivial API that can be dealt
with in a few lines of code. Thus, the external `recaptcha` php library is now
gone.

This API is…