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After recent changes, SigninManager exposes no public API surfaces
over SigninManagerBase. This CL eliminates nearly all usage of
signin_manager.h and in particular eliminates the no-longer needed
SigninManager::FromSigninManagerBase() method.

The remaining usage is for sites that *construct* SigninManager
instances. These sites will need to remain as such until SigninManager
is actually merged into SigninManagerBase.

This is a step in eliminating the inheritance relationship between
SigninManager and SigninManagerBase, as motivated in this design doc:

https://docs.google.com/document/d/15y-Db27BV08vrIyelHB-3CwiAfDYh-FigNKGXrqSWto/edit#heading=h.8jjdy95t6p7x

and described concretely here:

https://docs.google.com/document/d/15y-Db27BV08vrIyelHB-3CwiAfDYh-FigNKGXrqSWto/edit#heading=h.mbkrv9nkb93w

TBR=rohitrao@chromium.org

Bug: 952766, 883648
Change-Id: Icb114b11dc2c74d8b49cfd77baba33b707a4157e
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1565316
Commit-Queue: Colin Blundell <blundell@chromium.org>
Reviewed-by: Mihai Sardarescu <msarda@chromium.org>
Cr-Commit-Position: refs/heads/master@{#665898}