Taking this one, since I've already started to work on the dependencies (e.g. BrowsingDataCounterUtils), even though it might take a bit before I actually propose a CL for it.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/ebaf6fb99f5992c82f731ac8b2ff4b30a55b76e4

commit ebaf6fb99f5992c82f731ac8b2ff4b30a55b76e4
Author: Antonio Gomes <tonikitoo@igalia.com>
Date: Thu Nov 08 11:33:33 2018

[s13n] Convert c/b/ui/views/profiles/profile_chooser_view.cc to IdentityManager

CL also converts ::GetMessagesForAvatarSyncError defined at c/b/sync/sync_ui_util.h|cc,
(but not the whole file).

BUG= 890804 , 890796 

Change-Id: I4d7dbbdb1c5ca6f86e44cf9b4b454143eac08d9d
Reviewed-on: https://chromium-review.googlesource.com/c/1324589
Commit-Queue: Antonio Gomes <tonikitoo@igalia.com>
Reviewed-by: Thomas Tangl <tangltom@chromium.org>
Reviewed-by: Marc Treib <treib@chromium.org>
Reviewed-by: Colin Blundell <blundell@chromium.org>
Cr-Commit-Position: refs/heads/master@{#606415}
[modify] https://crrev.com/ebaf6fb99f5992c82f731ac8b2ff4b30a55b76e4/chrome/browser/sync/sync_ui_util.cc
[modify] https://crrev.com/ebaf6fb99f5992c82f731ac8b2ff4b30a55b76e4/chrome/browser/sync/sync_ui_util.h
[modify] https://crrev.com/ebaf6fb99f5992c82f731ac8b2ff4b30a55b76e4/chrome/browser/ui/views/profiles/avatar_toolbar_button.cc
[modify] https://crrev.com/ebaf6fb99f5992c82f731ac8b2ff4b30a55b76e4/chrome/browser/ui/views/profiles/profile_chooser_view.cc

 Issue 890794  has been merged into this issue.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/bb012abfe8bf1ea39b0e2cf5115849cafb78ab0a

commit bb012abfe8bf1ea39b0e2cf5115849cafb78ab0a
Author: Antonio Gomes <tonikitoo@igalia.com>
Date: Mon Nov 26 23:41:21 2018

[s13n] Convert arc_auth_service.cc to use IdentityManager

CL also partially needed to touch bits on signin_ui_util.cc|h
and people_handler.cc, both files properly listed on the BUG=
line below.

BUG= 907486 , 898810 , 890796 

Change-Id: Ic0d39cb14e100ae10375f66ca51fd526f3b2d64a
Reviewed-on: https://chromium-review.googlesource.com/c/1348674
Reviewed-by: Mihai Sardarescu <msarda@chromium.org>
Reviewed-by: Demetrios Papadopoulos <dpapad@chromium.org>
Reviewed-by: Yury Khmel <khmel@chromium.org>
Commit-Queue: Antonio Gomes <tonikitoo@igalia.com>
Cr-Commit-Position: refs/heads/master@{#610979}
[modify] https://crrev.com/bb012abfe8bf1ea39b0e2cf5115849cafb78ab0a/chrome/browser/chromeos/arc/auth/arc_auth_service.cc
[modify] https://crrev.com/bb012abfe8bf1ea39b0e2cf5115849cafb78ab0a/chrome/browser/signin/signin_ui_util.cc
[modify] https://crrev.com/bb012abfe8bf1ea39b0e2cf5115849cafb78ab0a/chrome/browser/signin/signin_ui_util.h
[modify] https://crrev.com/bb012abfe8bf1ea39b0e2cf5115849cafb78ab0a/chrome/browser/ui/webui/settings/people_handler.cc

I think we can be now at a point where we can actually implement this one, which is blocking at 898810 and 892155 => started

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/ff27eb0ead76487eae3c050c57f4b6ba56f6f945

commit ff27eb0ead76487eae3c050c57f4b6ba56f6f945
Author: Antonio Gomes <tonikitoo@igalia.com>
Date: Wed Dec 12 23:06:00 2018

Convert chrome/browser/sync/sync_ui_util.cc to IdentityManager

Also update all the callers and adapt the unit tests to stop using a custom
FakeSigninManagerBase and PO2TS, using IdentityManager and related test
utilities (e.g. IdentityTestEnvironment, PrimaryAccountMutator) instead,
so that the actual code being ported to can be tested. This means that
the STATUS_CASE_AUTHENTICATING case can't be tested anymore for ChromeOS,
but hopefully that should not be an issue since ChromeOS doesn't support
signin-in/out the primary account anyway.

Bug:  890796 
Change-Id: Iadcb5440eef126a801dd6c0cd145cbbe0bfb0b6d
Reviewed-on: https://chromium-review.googlesource.com/c/1362902
Reviewed-by: Toni Baržić <tbarzic@chromium.org>
Reviewed-by: Sylvain Defresne <sdefresne@chromium.org>
Reviewed-by: Marc Treib <treib@chromium.org>
Reviewed-by: Joshua Bell <jsbell@chromium.org>
Reviewed-by: Colin Blundell <blundell@chromium.org>
Reviewed-by: Mikel Astiz <mastiz@chromium.org>
Reviewed-by: Peter Kasting <pkasting@chromium.org>
Commit-Queue: Mario Sanchez Prada <mario@igalia.com>
Cr-Commit-Position: refs/heads/master@{#616094}
[modify] https://crrev.com/ff27eb0ead76487eae3c050c57f4b6ba56f6f945/chrome/browser/browsing_data/counters/browsing_data_counter_utils.cc
[modify] https://crrev.com/ff27eb0ead76487eae3c050c57f4b6ba56f6f945/chrome/browser/extensions/api/browsing_data/browsing_data_api.cc
[modify] https://crrev.com/ff27eb0ead76487eae3c050c57f4b6ba56f6f945/chrome/browser/extensions/api/browsing_data/browsing_data_test.cc
[modify] https://crrev.com/ff27eb0ead76487eae3c050c57f4b6ba56f6f945/chrome/browser/sync/sync_ui_util.cc
[modify] https://crrev.com/ff27eb0ead76487eae3c050c57f4b6ba56f6f945/chrome/browser/sync/sync_ui_util.h
[modify] https://crrev.com/ff27eb0ead76487eae3c050c57f4b6ba56f6f945/chrome/browser/sync/sync_ui_util_unittest.cc
[modify] https://crrev.com/ff27eb0ead76487eae3c050c57f4b6ba56f6f945/chrome/browser/ui/views/profiles/avatar_toolbar_button.cc
[modify] https://crrev.com/ff27eb0ead76487eae3c050c57f4b6ba56f6f945/chrome/browser/ui/views/profiles/profile_chooser_view.cc
[modify] https://crrev.com/ff27eb0ead76487eae3c050c57f4b6ba56f6f945/chrome/browser/ui/webui/settings/people_handler.cc
[modify] https://crrev.com/ff27eb0ead76487eae3c050c57f4b6ba56f6f945/chrome/browser/ui/webui/settings/settings_clear_browsing_data_handler.cc

 Issue 890797  has been merged into this issue.

 Issue 887873  has been merged into this issue.