[Android][Test] Refactor SignInWithSyncSetupAsIncomplete in SyncTestRule

This CL refactors the method
SyncTestRule#setUpTestAccountAndSignInWithSyncSetupAsIncomplete() by
replacing its internal sign-in method with sign-in from
AccountManagerTestRule.

Bug: 1126814
Change-Id: Ief0190f97ca45582bf6e9810f56f646aa49414e5
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2403461
Commit-Queue: Alice Wang <aliceywang@chromium.org>
Reviewed-by: Marc Treib <treib@chromium.org>
Cr-Commit-Position: refs/heads/master@{#806100}

chrome/android/javatests/src/org/chromium/chrome/browser/sync/SyncTestRule.java

@@ -214,8 +214,10 @@ public class SyncTestRule extends ChromeActivityTestRule<ChromeActivity> {
      * @return the test account that is signed in.
      */
     public Account setUpTestAccountAndSignInWithSyncSetupAsIncomplete() {
-        Account account = addTestAccount();
-        signinAndEnableSyncInternal(account, false);
+        Account account =
+                mAccountManagerTestRule.addAndSignInTestAccount(/* profileSyncService= */ null);
+        enableUKM();
+        SyncTestUtil.waitForSyncTransportActive();
         return account;
     }
 
@@ -412,6 +414,10 @@ public class SyncTestRule extends ChromeActivityTestRule<ChromeActivity> {
         return null;
     }
 
+    /**
+     * TODO(https://crbug.com/1126814): Remove this method once all its usages are migrated.
+     */
+    @Deprecated
     private void signinAndEnableSyncInternal(final Account account, boolean setFirstSetupComplete) {
         TestThreadUtils.runOnUiThreadBlocking(() -> {
             IdentityServicesProvider.get()