Manage Subscriptions button in URL bar should honor opt-in flows, when it's enabled by default

[stephendonner]

Description

Manage Subscriptions button in URL bar should honor opt-in flows, when it's enabled by default

This is a follow-on issue to #26705. After we've disabled the Manage Subscriptions button in the URL via that issue, we should have a plan to bring it back and provide the opt-in experience through the button, which then should also be enabled by default.

Steps to Reproduce

1. install 1.47.65
2. launch Brave
3. open brave://flags
4. set brave://flags/#brave-news-subscribe-button to Enabled
5. click Relaunch
6. dismiss the cookie-consent dialog
7. open a new-tab page
8. scroll
9. confirm you are not opted-in to Brave News
10. load planet.mozilla.org
11. wait
12. click on the Manage Subscriptions icon in the URL bar

Actual result:

No opt-in flow is triggered when clicking on the Manage Subscriptions button in the URL bar

Follow	Unfollow

Expected result:

Clicking on the Manage Subscriptions button should bring up some sort of opt-in flow, for first-time users.

Reproduces how often:

100%

Brave version (brave://version info)

Brave	1.47.65 Chromium: 107.0.5304.110 (Official Build) nightly (x86_64)
Revision	2a558545ab7e6fb8177002bf44d4fc1717cb2998-refs/branch-heads/5304@{#1202}
OS	macOS Version 11.7.1 (Build 20G918)

Version/Channel Information:

• Can you reproduce this issue with the current release? No
• Can you reproduce this issue with the beta channel? Yes
• Can you reproduce this issue with the nightly channel? Yes

cc @petemill @fallaciousreasoning @mattmcalister @LaurenWags @MadhaviSeelam