Connect refactored update flow to the new release notes page

[quanganhdo]

Task/Issue URL: https://app.asana.com/0/1199230911884351/1208183525704010/f
Tech Design URL:
CC:

Description:

Integrates with the new release note screen.

Steps to test this PR:

1. Refer to https://app.asana.com/0/1201037661562251/1208230039908704/f and use this build to check the behaviour: https://staticcdn.duckduckgo.com/macos-desktop-browser/a81f9679-e41d-404d-81a6-fd4a461d82f7/testbuilds/4be252d/duckduckgo-1.110.0.283.dmg

Definition of Done:

• Does this PR satisfy our Definition of Done?

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Internal references:

Pull Request Review Checklist
Software Engineering Expectations
Technical Design Template
Pull Request Documentation

[quanganhdo]

Warning

This pull request is not mergeable via GitHub because a downstack PR is open. Once all requirements are satisfied, merge this PR as a stack on Graphite.
Learn more

• Connect refactored update flow to the new release notes page #3411 👈
• Refactor automatic update flow to use custom Sparkle user driver #3274 : 2 other dependent PRs (#3275 , #3344 )
• main

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