[iOS] Clean deps and public_deps.

ios/public/provider/chrome/browser/build_config.gni

 # Copyright 2016 The Chromium Authors. All rights reserved.
 # Use of this source code is governed by a BSD-style license that can be
 # found in the LICENSE file.
 
 import("//build/config/chrome_build.gni")
 
 _default_ios_launchscreen_assets_target =
     "//ios/chrome/app/resources:launchscreen_assets"
 _default_ios_provider_target = "//ios/chrome/browser/providers:provider_factory"
 
 declare_args() {
-  # Control the provider API implementation used by Chromium on iOS. Requires
-  # access to the private Google-internal Chrome on iOS repository if true.
-  # DEPRECATED, will be removed as soon as all downstream code stops using it.
-  use_ios_internal_provider = is_chrome_branded
-
   # Label of the target providing image assets for the launchscreen.  This
   # target must be an asset catalog that contains at least two imagesets, one
   # named "launchscreen_app_logo" and one named "launchscreen_brand_name".
   ios_launchscreen_assets_target = _default_ios_launchscreen_assets_target
 
   # Label of the target providing implementation for ChromeBrowserProvider.
   # Overridden when using the Google-internal repository to build Chrome on iOS.
   ios_provider_target = _default_ios_provider_target
 }
 
 # True if the provider target used has not been overridden.
 use_default_ios_provider = ios_provider_target == _default_ios_provider_target