Signin: Restructure //components/signin/core/browser:shared

This CL moves the files that are currently in the
//components/signin/core/browser:shared GN target into the structure
described in this document:

https://docs.google.com/document/d/1p_kahITGFgv7PehQ61-thRVR3Hrdaf3tLryMytTRPYs/edit#

Namely, files intended for usage by the entire signin component and its
consumers are moved into a new //signin/public/base/ directory. Files
that are conceptually part of the IdentityManager public interface are
moved into //signin/public/identity_manager/.

This change was done in two parts:

1. A script that did the code moves and corresponding renames,
   include path changes, etc.
2. Manual followup that changed GN files and DEPS to reflect the new
   structure.

For ease of reviewing, I uploaded 1 as the original PS and 2 as PS2.

[email protected]

Bug: 952788
Change-Id: I88afc79b426f3acc954d78006ed88d4cd0579672
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/1687239
Reviewed-by: Colin Blundell <[email protected]>
Reviewed-by: Jochen Eisinger <[email protected]>
Reviewed-by: Mihai Sardarescu <[email protected]>
Commit-Queue: Colin Blundell <[email protected]>
Cr-Commit-Position: refs/heads/master@{#676329}
diff --git a/chrome/browser/extensions/api/identity/identity_api.h b/chrome/browser/extensions/api/identity/identity_api.h
index 23bc6ed..d766319 100644
--- a/chrome/browser/extensions/api/identity/identity_api.h
+++ b/chrome/browser/extensions/api/identity/identity_api.h
@@ -29,7 +29,7 @@
 #include "chrome/browser/extensions/api/identity/identity_remove_cached_auth_token_function.h"
 #include "chrome/browser/extensions/api/identity/web_auth_flow.h"
 #include "chrome/browser/extensions/chrome_extension_function.h"
-#include "components/signin/core/browser/signin_buildflags.h"
+#include "components/signin/public/base/signin_buildflags.h"
 #include "components/signin/public/identity_manager/identity_manager.h"
 #include "extensions/browser/browser_context_keyed_api_factory.h"
 #include "extensions/browser/event_router.h"