[profiles] Profile picker listen for hosted domain changes

An observer for hosted domain changes was added in CL:
https://chromium-review.googlesource.com/c/chromium/src/+/2568285/4/chrome/browser/profiles/profile_info_cache_observer.h

The profile picker has UI depending on the hosted domain and is intended
to dynamically update when profile changes.
To be consistent with other profile-related events, this CL updates the
picker when the hosted domain changes as well.

Bug: None
Change-Id: Ia0f7a19c23d8f6c86d3358a4ecc58787877597d4
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2569514Reviewed-by: Monica Basta <msalama@chromium.org>
Commit-Queue: David Roger <droger@chromium.org>
Cr-Commit-Position: refs/heads/master@{#837534}

chrome/browser/ui/webui/signin/profile_picker_handler.cc

@@ -627,6 +627,11 @@ void ProfilePickerHandler::OnProfileNameChanged(
   PushProfilesList();
 }
 
+void ProfilePickerHandler::OnProfileHostedDomainChanged(
+    const base::FilePath& profile_path) {
+  PushProfilesList();
+}
+
 void ProfilePickerHandler::DidFirstVisuallyNonEmptyPaint() {
   DCHECK(!creation_time_on_startup_.is_null());
   base::UmaHistogramTimes("ProfilePicker.StartupTime.FirstPaint",

chrome/browser/ui/webui/signin/profile_picker_handler.h

@@ -73,6 +73,8 @@ class ProfilePickerHandler : public content::WebUIMessageHandler,
       const base::FilePath& profile_path) override;
   void OnProfileNameChanged(const base::FilePath& profile_path,
                             const base::string16& old_profile_name) override;
+  void OnProfileHostedDomainChanged(
+      const base::FilePath& profile_path) override;
 
   // content::WebContentsObserver:
   void DidFirstVisuallyNonEmptyPaint() override;