[Brave News]: Subscribe button shouldn't show unless the user has opted in to Brave News.

[fallaciousreasoning]

1. Don't opt in to Brave News
2. Visit a site with an RSS feed

Actual
The subscribe button shows up

Expected
The subscribe button does not show up because the user hasn't opted in to Brave News

[btlechowski]

@rebron @LaurenWags @kjozwiak This fix needs an uplift to 1.47.x as it fixes many issues.

Issue 1: Unable to subscribe to feed through Brave News subscribe button on clean install
Unable to subscribe to first feed

Issue 2: Blank page after subscribing to a feed and enabling Brave news

[rebron]

@fallaciousreasoning @petemill Can we get uplifts for this for 1.47.x and 1.46.x?

[fallaciousreasoning]

1.46.x: brave/brave-core#16265
1.47.x: brave/brave-core#16266

[kjozwiak]

The above requires 1.47.120 or higher for 1.47.x verification 👍

[stephendonner]

Verified PASSSED using

Brave	1.47.120 Chromium: 108.0.5359.99 (Official Build) dev (x86_64)
Revision	410951fc34bb4b2cbf182231f9f779efaafaf682-refs/branch-heads/5359_71@{#9}
OS	macOS Version 13.1 (Build 22C65)

Steps:

1. installed 1.47.120
2. launched Brave
3. opened brave://flags
4. ensured there's no flag for the Brave News button
5. loaded theatlantic.com
6. ensured there's no Manage Subscriptions button visible in the URL bar
7. opened a new-tab page
8. ensured the Brave News opt-in page is still there
9. clicked on Customize
10. clicked on Brave News
11. ensured the Brave News opt-in page is still there
12. clicked on Show Brave News
13. returned to theatlantic.com tab
14. confirmed the Manage Subscriptions RSS-feed icon is in the URL bar

Confirmed the Manage Subscriptions RSS-feed icon isn't visible until opted-in to Brave News

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