Add NTP search promo P3A question

[DJAndries]

Resolves brave/brave-browser#24065

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
• Squashed any review feedback or "fixup" commits before merge, so that history is a record of what happened in the repo, not your PR
• 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:

Regression testing of brave/brave-browser#23191 recommended.

1. Launch browser using --enable-features="BraveSearchNTP" switch, with fresh profile.
2. Access brave://local-state, ensure Brave.Search.Promo.NewTabPage does not exist.
3. Access brave://settings/search, change search engine to something other than Brave.
4. Ensure sponsored images are disabled and access new tab page, ensure promo appears.
5. Check local state, the metric should now exist, and should be set to 0.
6. Make search query via NTP promo.
7. Metric should have a value of 1.
8. Change the default search engine to Brave by either clicking on the prompt that appears on the search engine results page, or via brave://settings/search (may be good to test both).
9. Relevant metric should have a value of 3.
10. Start over with a fresh profile, see promo but do not perform a search.
11. Change search engine to Brave via one of the methods in step 8. (Accessing https://search.brave.com/search?q=test&action=makeDefault directly will force the SERP prompt to show up.)
12. Relevant metric should have a value of 2.

[simonhong]

This is called whenever NTP is created if promotion is enabled.
However, NTP will not show promotion when sponsored images are displayed.
When sponsored images are displayed, this should not be called.
I'll push another commit.

[simonhong]

Pushed 0e00a36

[simonhong]

++ first commit :)

[simonhong]

Kindly ping @iefremov :)