Hide original tab search button when pref is off

[sangwoo108]

When the preference is turned off, we shouldn't show the button

Resolves brave/brave-browser#30829

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 wiki
  • npm run lint, 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/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:

This applies to only non-win10 platform.

Manual

• Turn off tab search button from brave://settings/appearance
• open up a new window - tab search button shouldn't be on the new window
• Toggle vertical tab strip on and off - tab search button shouldn't reappear

Automated

VerticalTabStripBrowserTest.OriginalTabSearchButton

[fallaciousreasoning]

LGTM

[kjozwiak]

Verification PASSED on macOS 13.4 Ventura x64 using the following build(s):

Brave | 1.54.54 Chromium: 114.0.5735.110 (Official Build) nightly (x86_64)
--- | ---
Revision | 1c828682b85bbc70230a48f5e345489ec447373e-refs/branch-heads/5735_90@{#13}
OS | macOS Version 13.4 (Build 22F66)

Reproduced the original issue using the STR/Cases outlined via brave/brave-browser#30829 (comment) running 1.54.47 Chromium: 114.0.5735.110 as per the following:

• Disabled Show tab search button and the button was still appearing when opening new windows

Using the STR/Cases outlined via brave/brave-browser#30829 (comment), verified that the search button was being removed correctly as per the following:

• ensured that toggling Show tab search button via brave://settings/appearance correctly removes the search button
  • ensured it's being removed from the current active window
  • ensured it's being removed from all other currently opened windows
  • ensured it's not being added when opening new windows
• ensured that the Show tab search button state is persistent (not being enabled/disabled when it shouldn't)
  • ensured that the Show tab search button state is persistent across several restarts

As discussed with @rebron via https://bravesoftware.slack.com/archives/CHGKGMHDJ/p1686290856620189, the Search button does not get removed from vertical tabs when enabled. Essentially toggling Show tab search button doesn't do anything on macOS when vertical tabs are enabled.