[Brave News] Fix bug where direct feeds didn't show up as followed

[fallaciousreasoning]

Follow up for #15963, which fixed it's original issue but broke the button toggle state.

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. With #brave-news-subscribe-button enabled
2. Navigate to theatlantic.com
3. Follow Best of the Atlantic
4. The button state should update

[simonhong]

++

[stephendonner]

While initially trying to test this for uplift, I encountered brave/brave-browser#27052, just FYI for now.

[stephendonner]

Verified PASSED using

Brave	1.48.15 Chromium: 108.0.5359.62 (Official Build) nightly (x86_64)
Revision	041930a89a990cfab0315a2d9f20d6429a4a67cf-refs/branch-heads/5359@{#938}
OS	macOS Version 11.7.1 (Build 20G918)

Steps:

1. installed 1.48.15
2. launched Brave
3. opened brave://flags
4. confirmed no Brave News button flag exists
5. loaded theatlantic.com
6. clicked on the RSS-feed icon in the URL bar
7. clicked on Best of the Atlantic 's Follow button
8. waited

Confirmed the Follow / Unfollow button state is accurately reflected

brave://flags	theatlantic.com	Follow	Unfollow

NOTE: logged brave/brave-browser#27052 while testing

[fallaciousreasoning]

Note: I think brave/brave-browser#27052 was introduced by #16038, so the fix for that will need an uplift too.