Revert "Use new mailto handling setup API."

This reverts commit 20a36a40.

Reason for revert: New API fails under unrelated tests.  Rolling back to old API until this can be fixed.

Original change's description:
> Use new mailto handling setup API.
> 
> Re-lands https://chromium-review.googlesource.com/1031050 after
> fixes to downstream changes.
> 
> Bug: 810904
> Cq-Include-Trybots: master.tryserver.chromium.mac:ios-simulator-cronet;master.tryserver.chromium.mac:ios-simulator-full-configs
> Change-Id: I2cb00c90d6d35cb7c4dd5cb8ac7c5ffb8746894f
> Reviewed-on: https://chromium-review.googlesource.com/1033019
> Reviewed-by: Peter Lee <pkl@chromium.org>
> Commit-Queue: Daniel Blakemore <danblakemore@google.com>
> Cr-Commit-Position: refs/heads/master@{#554422}

TBR=pkl@chromium.org,danblakemore@google.com

Change-Id: Ib56bde2e2f8c608e67982507923110747e62f9fa
No-Presubmit: true
No-Tree-Checks: true
No-Try: true
Bug: 810904
Cq-Include-Trybots: master.tryserver.chromium.mac:ios-simulator-cronet;master.tryserver.chromium.mac:ios-simulator-full-configs
Reviewed-on: https://chromium-review.googlesource.com/1033547Reviewed-by: Peter Lee <pkl@chromium.org>
Commit-Queue: Peter Lee <pkl@chromium.org>
Cr-Commit-Position: refs/heads/master@{#554537}

ios/chrome/app/main_controller.mm

@@ -1126,19 +1126,24 @@ void MainControllerAuthenticationServiceDelegate::ClearBrowsingData(
 
 - (void)initializeMailtoHandling {
   if (base::FeatureList::IsEnabled(kMailtoHandledWithGoogleUI)) {
-    __weak __typeof(self) weakSelf = self;
     [[DeferredInitializationRunner sharedInstance]
         enqueueBlockNamed:kMailtoHandlingInitialization
                     block:^{
-                      __strong __typeof(weakSelf) strongSelf = weakSelf;
-                      if (!strongSelf) {
-                        return;
-                      }
                       MailtoHandlerProvider* provider =
                           ios::GetChromeBrowserProvider()
                               ->GetMailtoHandlerProvider();
+                      ios::ChromeIdentityService* identityService =
+                          ios::GetChromeBrowserProvider()
+                              ->GetChromeIdentityService();
                       provider->PrepareMailtoHandling(
-                          strongSelf->_mainBrowserState);
+                          ^ChromeIdentity* {
+                            // TODO:(crbug.com/810904) Replace with currently
+                            // signed-in user.
+                            return nil;
+                          },
+                          ^NSArray<ChromeIdentity*>* {
+                            return identityService->GetAllIdentities();
+                          });
                     }];
   }
 }