[ios] Use ProfileAttributesIOS API of ProfileAttributesStorageIOS

With https://crrev.com/c/5797218, ProfileAttributesStorageIOS exposes
a new API to get/set the attributes about a Profile stored in local
preferences.

This CL convert //ios/chrome/browser/signin to use the new API
instead of the old one.

Bug: 359522668
Change-Id: Ic3ea0e1a87792ebfc0826f2f7efd521c5d87de0d
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5803990
Auto-Submit: Sylvain Defresne <sdefresne@chromium.org>
Commit-Queue: Sylvain Defresne <sdefresne@chromium.org>
Reviewed-by: Marc Treib <treib@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1345879}