Don't show favicon when alert indicator is visible

[sangwoo108]

We shouldn't show both of them at the same time

Resolves brave/brave-browser#30021

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:

• Play a video from a tab
• Activate another tab
• Make vertical tabs collapsed
  • Favicon of the tab that is playing video shouldn't be visible
  • Only speaker button should be visible.

[MadhaviSeelam]

Verification PASSED using

Brave | 1.53.19 Chromium: 113.0.5672.77 (Official Build) nightly (64-bit)
-- | --
Revision | c4236862955e005c2187105415ac4a2ecf86dff1-refs/branch-heads/5672_62@{#3}
OS | Windows 11 Version 22H2 (Build 22621.1555)

1. Install 1.53.19
2. launched Brave
3. clicked Skip >> Skip >> Finish
4. visited youtube.com (and couple of other audio playing sites)
5. enabled vertical tabs via context menu
6. played audio which is not the active tab
7. mute/unmute audio playing tabs

Confirmed favicon is not shown for audio playing tab in collapsed state in the vertical tab panel

speaker button is visible while mute/unmute on the audio playing tab

Dark mode

Example	Example	Example	Example

Example	Example