Resolve QSE youtube search on upgrade

[deeppandya]

Resolves brave/brave-browser#42567

Submitter Checklist:

• I confirm that no security/privacy review is needed and no other type of reviews are needed, or that I have requested them
• 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 wiki
  • npm run presubmit wiki, 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/Web-Compatibility-Exceptions-in-Brave
  • https://github.com/brave/brave-browser/wiki/QA-Guide
  • https://github.com/brave/brave-browser/wiki/P3A

Test Plan:

[samartnik]

lgtm

[brave-builds]

Released in v1.75.154

[hffvld]

Verified on Pixel 7 using version(s):

Device/OS: Pixel 7 / panther_beta-user 15 BP11.241025.006 release-keys
Brave build: 1.76.1 
Chromium: 132.0.6834.57 (Official Build) canary (64-bit) 

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STEPS:

1. Install old Brave build where the YT search thumbnail is not shown in the QSE bar, in my case Nighlty 1.75.1
2. Launch Brave > Go through onboarding
3. Open NTP > Tap in the URL search bar
4. Type a query > Confirm that YT search thumbnail is not shown
5. Tap ⚙️ icon > Confirm that YT search is not shown
6. Upgrade Brave to Nightly 1.76.1 or higher
7. Launch Brave > Type a query again > Verify that YT search thumbnail is shown
8. Tap ⚙️ icon > Verify that YT is shown
9. Close the QSE settings > Type a query again
10. Use YT to make a search > Verify that the search results opened with https://youtube.com

ACTUAL RESULTS:

• Verified that the YT search thumbnail is shown in the QSE bar after the Brave upgrade.
• Verified that the YT search is shown in the QSE settings after the Brave upgrade.
• Verified that the search results opened with https://youtube.com when using YT search on the QSE bar.

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2025-01-09_10-59-39.mp4