Support [Get/Set]BrowserProfileType on iOS.

Profile type on other platforms is assigned and retrieved by
|profile_metrics::[Get/Set]BrowserProfileType| functions.
This is now supported on iOS and all use cases of |GetBrowserStateType|
are replaced with |GetBrowserProfileType|.

Bug: 1169142
Change-Id: Ic81948e6d5e33a3f5f349d7f617be583c764afce
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2840463
Reviewed-by: Sylvain Defresne <sdefresne@chromium.org>
Commit-Queue: Ramin Halavati <rhalavati@chromium.org>
Cr-Commit-Position: refs/heads/master@{#875124}
GitOrigin-RevId: f87d28cc1821e4ec54e104045243a24bbc799440
12 files changed