[Profiles] Make DestroyProfileOnBrowserClose work with Background Mode

Don't run DestroyProfileOnBrowserClose logic if Background Mode is
enabled, i.e. wait for the entire browser to exit before destroying
the Profile object.

Bug: 88586, 566835
Change-Id: I593d5537fc494bab1cd435b65cfc57075d92cfe2
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2476173Reviewed-by: Mihai Sardarescu <msarda@chromium.org>
Commit-Queue: Nicolas Ouellet-Payeur <nicolaso@chromium.org>
Cr-Commit-Position: refs/heads/master@{#819437}

chrome/browser/profiles/profile_manager.cc

@@ -1886,14 +1886,18 @@ void ProfileManager::OnBrowserClosed(Browser* browser) {
   if (profile->IsGuestSession() || profile->IsEphemeralGuestProfile())
     CleanUpGuestProfile();
 
+  ProfileAttributesEntry* entry;
+  bool background_mode =
+      GetProfileAttributesStorage().GetProfileAttributesWithPath(
+          profile->GetPath(), &entry) &&
+      entry->GetBackgroundStatus();
   if (base::FeatureList::IsEnabled(features::kDestroyProfileOnBrowserClose) &&
       !profile->IsOffTheRecord() &&
-      !profile->GetPrefs()->GetBoolean(prefs::kForceEphemeralProfiles)) {
+      !profile->GetPrefs()->GetBoolean(prefs::kForceEphemeralProfiles) &&
+      !background_mode) {
     // TODO(crbug.com/88586): Add EarlyProfileCleanup support for Guest and
     // Ephemeral profiles.
 
-    // TODO(crbug.com/88586): Make sure this works with Background Mode.
-
     // Post a task to remove the Profile, so other OnBrowserClosed() hooks and
     // the destructor for Browser can run without referencing a deleted Profile.
     content::GetUIThreadTaskRunner({})->PostTask(