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This change is a follow up to a previous Chrome SSO change[1]. Currently, Chrome SSO through GCPW would only work if the profile is the initial profile dir. That wouldn't work if initial profile dir is deleted and/or another profile is being used. This change addresses signing into profile through GCPW regardless of profile being initial profile.

Note that signing into profile doesn't work:

If the same GCPW user is authenticated in any other profile.
If any other profile was used to sign-in with GCPW before.
[1] https://chromium-review.googlesource.com/c/chromium/src/+/1984474

Bug: 1038368
Change-Id: I8719d1dbea59eb31206f9c897331fcd9674aae9b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2084721
Commit-Queue: Yusuf Sengul <yusufsn@google.com>
Reviewed-by: Rakesh Soma <rakeshsoma@google.com>
Reviewed-by: Mihai Sardarescu <msarda@chromium.org>
Reviewed-by: Roger Tawa <rogerta@chromium.org>
Cr-Commit-Position: refs/heads/master@{#756429}