Hide Vertical Tab strip widget when disabled

[sangwoo108]

On Mac, the vertical tab strip widget shows up when restoring the browser window. This is because upstream implementation makes all child widgets regardless of their previous visibility.

In order to fix that, observes the widget's visibility and double-check it should be visible.

Resolves brave/brave-browser#29917

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:

Manually testable on Mac(without stage manager)

• context-click on a tab and choose Use Vertical Tabs
• now, context-click again and deselect Use Vertical Tabs to return to the default mode
• minimize Brave (but don't shut it down)
• restore the window
• examine the left panel

[stephendonner]

Verified PASSED using

Brave	1.53.18 Chromium: 113.0.5672.77 (Official Build) nightly (x86_64)
Revision	c4236862955e005c2187105415ac4a2ecf86dff1-refs/branch-heads/5672_62@{#3}
OS	macOS Version 11.7.6 (Build 20G1231)

Steps:

1. installed 1.53.18
2. launch Brave
3. load a bunch of tabs
4. context-click on a tab and choose Use Vertical Tabs
5. now, context-click again and deselect Use Vertical Tabs to return to the default mode
6. minimize Brave (but don't shut it down)
7. restore the window
8. examine the left panel

Confirmed the tab-view orientation is correct, and there are NO flashes of the previous-orientation's content when switching between modes