Avoid late keyed services with TestingProfile

This patch migrates tests away from deprecated APIs and adopts
TestingProfile::Builder for tests in
/chrome/browser/search_engines.

Rationale: creating or overriding keyed services after the profile has
been created is problematic and known to cause hard-to-debug test
flakiness, because it bypasses BrowserContextDependencyManager and often
leading to use-after-free.

This CL was uploaded by git cl split.

R=orinj@chromium.org

Bug: 1106699
Change-Id: I40bb5c4a6624623f2548babc4ef8fed32566b9b9
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2316362
Auto-Submit: Mikel Astiz <mastiz@chromium.org>
Reviewed-by: Orin Jaworski <orinj@chromium.org>
Commit-Queue: Orin Jaworski <orinj@chromium.org>
Commit-Queue: Mikel Astiz <mastiz@chromium.org>
Cr-Commit-Position: refs/heads/master@{#791547}

chrome/browser/search_engines/template_url_service_unittest.cc

@@ -1224,7 +1224,6 @@ TEST_F(TemplateURLServiceWithoutFallbackTest, ManualCountrySpecificGoogleURL) {
 // Make sure TemplateURLService generates a KEYWORD_GENERATED visit for
 // KEYWORD visits.
 TEST_F(TemplateURLServiceTest, GenerateVisitOnKeyword) {
-  test_util()->profile()->CreateBookmarkModel(false);
   ASSERT_TRUE(test_util()->profile()->CreateHistoryService(true, false));
   test_util()->ResetModel(true);