SERP Settings Sync: Align feature flag names with other platforms

[mikescamell]

Task/Issue URL: https://app.asana.com/1/137249556945/project/1207908166761516/task/1211978534005008?focus=true

Description

This pull request refactors feature flag usage across the browser and DuckChat modules by replacing references to SettingsPageFeature with the new SerpSettingsFeature interface, and introduces a new toggle for controlling the visibility of the "Hide AI Generated Images" option in DuckChat settings.

Feature flag refactoring:

• Replaced all usages of SettingsPageFeature with SerpSettingsFeature in BrowserTabViewModel, DuckDuckGoRequestRewriter, dependency injection (BrowserModule), and related test files to standardize feature flag handling for SERP settings.
• Updated constructor parameters and usages in affected classes and test setups to use SerpSettingsFeature instead of SettingsPageFeature.
• Modified logic to use storeSerpSettings() from SerpSettingsFeature in place of serpSettingsSync() from SettingsPageFeature for feature checks.

DuckChat settings improvements:

• Added a new toggle showHideAiGeneratedImages() to DuckChatFeature to control visibility of the "Hide AI Generated Images" option in AI Features Settings. Updated DuckChatSettingsViewModel to use this toggle for UI logic and navigation.

Test updates:

• Updated all affected unit tests to use SerpSettingsFeature for feature flag mocking and assertions, ensuring consistency and coverage for the new interface and toggle.

Steps to test this PR

Hide AI Generated Images Toggle

• Enable showHideAiGeneratedImages feature toggle
• Open Settings -> AI Features
• Check AI-Generated Images option is visible
• Click it
• SERP Settings should open
• Disable showHideAiGeneratedImages feature toggle
• Open Settings -> AI Features
• Check AI-Generated Images option is NOT visible

storeSerpSettings Toggle

• Clear data and launch app
• Enable storeSerpSettings feature toggle
• Navigate to "Duck AI Testing url" listed here
• Do a search e.g. "FPL"
• Filter logs for "SERP-SETTINGS"
• Check IsNativeDuckAiEnabledHandler has fired
• Open Settings
• Press back
• In the logs SubscriptionEventData should be sent
• Click SERP settings cog
• Click "Manage" by "AI Features"
• Click "Open Duck.ai Settings"
• Check logs for "OpenNativeSettingsHandler" and native AI Features screen should open
• Navigate to "SERP Settings Testing URL"
• Do a search e.g. "FPL"
• Check GetNativeSettingsHandler fires
• Check UpdateNativeSettingsHandler fires

UI changes

N/A

[mikescamell]

• SERP Settings Sync: Align feature flag names with other platforms #7159 👈 (View in Graphite)
• SERP Settings Sync: Hide SERP duck.ai toggle  #7153
• SERP Settings Sync: Add and update pixels #7073
• develop

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[marcosholgado]

LGTM