Replaced chrome dark logo with channel product logo from settings drawer menu

[simonhong]

fix brave/brave-browser#31355

Resolves

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 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:

[simonhong]

@rebron this looks fine?

[rebron]

@rebron this looks fine?

Should we use the Gear icon for Settings instead?
cc: @aguscruiz

[aguscruiz]

@simonhong can you use the regular Brave logo in dark mode too?
Not that outline one, but the one you used here:

[simonhong]

@simonhong can you use the regular Brave logo in dark mode too? Not that outline one, but the one you used here:

Ok, I'll try to put per-channel brave icon there.

[mkarolin]

@simonhong, can't we just copy our own svg over the upstream one in brave/build/commands/lib/util.js updateBranding?

[petemill]

@simonhong in your opinion, is this patch better than overwriting the file from util.js | updateBranding?

[simonhong]

@mkarolin @petemill Oh, right. we also could copy per-channel files before build. Done :)

[kjozwiak]

Verification PASSED on Win 11 x64 using the following build(s):

Brave | 1.60.59 Chromium: 117.0.5938.92 (Official Build) nightly (64-bit)
-- | --
Revision | a701506b269c40f7d8ad52ecf7dfaae15723ec94
OS | Windows 11 Version 22H2 (Build 22621.2283)

Using the STR/Cases outlined via brave/brave-browser#31355 (comment), ensured that the Chrome icon wasn't appearing via brave://extensions & brave://settings as per the following:

Case #1

Example	Example

Case #2

Example	Example