Rewrite component update service in terms of components/update_client.

The goal of this change is to re-implement the component updater by
reusing the common code in components/update_client while keeping
the its public interface the same as before, in order to minimize
changes in its existing clients.

BUG=450337

Review URL: https://codereview.chromium.org/1133443002

Cr-Commit-Position: refs/heads/master@{#331412}
diff --git a/components/update_client/task.h b/components/update_client/task.h
index 51b6890..52af7521 100644
--- a/components/update_client/task.h
+++ b/components/update_client/task.h
@@ -19,10 +19,9 @@
 // together.
 class Task {
  public:
-  using Callback = base::Callback<void(Task* task, int error)>;
   virtual ~Task() {}
 
-  virtual void Run(const Callback& callback) = 0;
+  virtual void Run() = 0;
 };
 
 }  // namespace update_client