Remove now-unused c/b/api/ directory.

chrome/browser/api/DEPS

-# The chrome/browser/api directory is for programming interfaces
-# provided by Chrome to Browser Components that run within Chrome.
-# Files here are not allowed to include stuff under chrome/browser
-# since that would leak implementation details to users of the APIs.
-#
-# APIs can be either pure-virtual to allow specialization at runtime,
-# or they can be non-virtual and specialized per platform (or
-# otherwise at compile time), or a mix of non-virtual and virtual.
-# The primary initial objective is to break Browser Components'
-# dependencies on implementation details, so non-virtual classes in
-# header files that do not expose any headers from chrome/browser
-# except for chrome/browser/api are acceptable.
-#
-# Note that for non-virtual APIs, there is an increased risk of an
-# implicit link-time dependency remaining from the user of the API to
-# the implementation.  We are accepting this risk initially, but plan
-# to write a new type of link-time or target-level set of dependency
-# rules to help us find such problems and reduce them over time.
-#
-# The directory structure under chrome/browser/api/ is a mirror of
-# those parts of the chrome/browser/ structure that APIs have been
-# extracted from.  Hence, an API defined in chrome/browser/api/x/y/z
-# is likely to be implemented in a directory chrome/browser/x/y/z.
-#
-# See http://www.chromium.org/developers/design-documents/browser-components
-include_rules = [
-  "-chrome/browser",
-  "+chrome/browser/api",
-]