[Brave News] Look for missing favicons in the FaviconService

[fallaciousreasoning]

Resolves brave/brave-browser#26266

Brave News Direct sources, with favicons

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 Brave News V2
2. Visit a page with a direct source (I like using https://reactjs.org/)
3. Add the direct source to Brave News
4. The source should have an icon

[brave-builds]

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

[petemill]

I haven't finished reviewing and testing, but just wanted to give initial feedback first

[brave-builds]

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

[fallaciousreasoning]

@petemill how does this look to you?

[brave-builds]

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

[petemill]

nit: I wonder if it avoids a re-render for subsequent (different) calls to useFavicon with the same publisherId if we initialize this state variable to the potential cache version, i.e. ... = React.useState(cache[publisherId])

[simonhong]

++ 👍🏼

[brave-builds]

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

[kjozwiak]

Verification's on Nightly were completed via #15820 (comment) before uplifting the above into 1.46.x.