brave-core Desktop NTP: no News peek when a sponsored wallpaper is present

Resolves https://github.com/brave/brave-browser/issues/34968

Submitter Checklist:

[x] I confirm that no security/privacy review is needed, or that I have requested one
[x] There is a ticket for my issue
[x] Used Github auto-closing keywords in the PR description above
[x] 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
[x] Added appropriate labels (QA/Yes or QA/No; release-notes/include or release-notes/exclude; OS/...) to the associated issue
[x] 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
[x] Ran git rebase master (if needed)

[x] A security review is not needed, or a link to one is included in the PR description
[x] New files have MPL-2.0 license header
[x] Adequate test coverage exists to prevent regressions
[x] Major classes, functions and non-trivial code blocks are well-commented
[x] Changes in component dependencies are properly reflected in gn
[x] Code follows the style guide
[x] Test plan is specified in PR before merging

[ ] 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