Add channel icons & update how channel cards look to be in line with the updated design.

[fallaciousreasoning]

Resolves brave/brave-browser#26115
Partially Resolves brave/brave-browser#25988

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, npm run lint, 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:

1. Enable the Brave News V2 flag
2. When customizing Brave News, channels should have the new icons.

[brave-builds]

A Storybook has been deployed to preview UI for the latest push

[sangwoo108]

Beautiful! LGTM.

[stephendonner]

Verified PASSED using

Steps:

1. installed 1.47.47
2. launched Brave
3. clicked on Skip welcome tour
4. opened brave://flags
5. set brave://flags/#brave-news-v2 to Enabled
6. clicked on Relaunch
7. opened a new-tab page
8. clicked on Customize
9. clicked on Brave News
10. clicked on Turn on Brave News
11. clicked on Show more beneath Channels

Confirmed the new icon set is in

Dark	Light