SearchEngineTracker: Re-enable DefaultSearchEngineP3A test.

[rillian]

This was disabled in 27bf9e3 for intermittent failures.
Add a call to wait for TemplateURLServiceFactory to finish
loading, and re-enable to see if that stabilizes the browser
test.

See brave/brave-browser#13057 for tracking.

This duplicates VerifyTemplateURLServiceLoad() from the
search_engine_provider browser test, but it's a small piece
of code and having two file-local implementations is simple
enough.

Resolves

Submitter Checklist:

• I confirm that no security/privacy review is needed, or that I have requested one
• There is a ticket for my issue
• Used Github auto-closing keywords in the PR description above
• Wrote a good PR/commit description
• Added appropriate labels (QA/Yes or QA/No; release-notes/include or release-notes/exclude; OS/...) to the associated issue
• Checked the PR locally: npm run test -- brave_browser_tests, npm run test -- brave_unit_tests, npm run lint, npm run gn_check, npm run tslint
• Ran git rebase master (if needed)

Reviewer Checklist:

• A security review is not needed, or a link to one is included in the PR description
• New files have MPL-2.0 license header
• Adequate test coverage exists to prevent regressions
• Major classes, functions and non-trivial code blocks are well-commented
• Changes in component dependencies are properly reflected in gn
• Code follows the style guide
• Test plan is specified in PR before merging

After-merge Checklist:

• The associated issue milestone is set to the smallest version that the
  changes has landed on
• All relevant documentation has been updated, for instance:
  • https://github.com/brave/brave-browser/wiki/Deviations-from-Chromium-(features-we-disable-or-remove)
  • https://github.com/brave/brave-browser/wiki/Proxy-redirected-URLs
  • https://github.com/brave/brave-browser/wiki/Fingerprinting-Protections
  • https://github.com/brave/brave-browser/wiki/Brave%E2%80%99s-Use-of-Referral-Codes
  • https://github.com/brave/brave-browser/wiki/Custom-Headers
  • https://github.com/brave/brave-browser/wiki/Web-Compatibility-Exceptions-in-Brave
  • https://github.com/brave/brave-browser/wiki/QA-Guide
  • https://github.com/brave/brave-browser/wiki/P3A

Test Plan:

[iefremov]

lgtm once we just use verbatim search_test_utils::WaitForTemplateURLServiceToLoad(service);

[rillian]

As far as I can tell, the intermittent macOS ci failures aren't related.

[bsclifton]

Nice work 😄 Thanks for getting these back in @rillian!