Fire Dialog: New clear actions

[0nko]

Task/Issue URL: https://app.asana.com/1/137249556945/project/1207418217763355/task/1212237611537705?focus=true

Description

This PR adds new data clearing actions that allow removing different data types independently (tabs, data, chats).

The affected interfaces are lower-level layer that responsible for performing individual data deletion.

Steps to test this PR

• Make sure all units tests pass

---

Note

Introduce granular data-clearing actions (tabs, browser data, chats) with DuckAI-targeted IndexedDB/localStorage clearing and update integrations/tests.

• APIs and Actions:
  • Add granular clear methods in ClearDataAction: clearTabsOnly, clearBrowserDataOnly, clearDuckAiChatsOnly; keep clearTabsAndAllDataAsync.
  • Extend WebDataManager with clearData(webView, webStorage, shouldClearBrowserData, shouldClearDuckAiData); update WebViewDataManager to support granular clearing, use SettingsDataStore.clearDuckAiData, and refine directory deletions/fallbacks.
• Storage Handling:
  • WebLocalStorageManager: new overload to clear selectively by flags; respects fireproofed domains and DuckAI keys/domains (duckduckgo.com, duck.ai).
  • IndexedDBManager: change to clearIndexedDB(shouldClearDuckAiData) and add clearOnlyDuckAiData; remove settings store dependency; preserve/exclude folders based on domains and flags.
• Integration:
  • AutomaticDataClearer / DataClearingWorker: switch to clearTabsOnly for tabs-only paths.
  • PrivacyModule: wire updated ClearPersonalDataAction (remove AdClickManager arg).
  • TabDataRepository.deleteAll: also clears previews, temp favicons, ad clicks, and webview sessions.
• Tests:
  • Add/expand tests across instrumentation and unit suites to cover granular clearing paths, DuckAI-specific behavior, IndexedDB/localStorage exclusions, fallbacks, and new repository deletions.

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[0nko]

• Fire Dialog: Translations #7383
• Fire Dialog: Granular fire bottom sheet #7359
• Fire Dialog: New data clearing component #7351
• Fire Dialog: New clear actions #7339 👈 (View in Graphite)
• Fire Dialog: New feature flag #7295
• Fire Dialog: Data storage #7282
• develop

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[cursor]

Cursor Agent can help with this pull request. Just @cursor in comments and I'll start working on changes in this branch.
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[CDRussell]

As I ask in Asana, it would be good to consider if there's any way to guard these changes with feature flags.

The settingsDataStore.clearDuckAiData check is one potential ANR introduction I've spotted, but hard to tell from reviewing just this PR if there's anything else.

I appreciate it's tricky to FF around changes like this, but can you create a task to consider how and if it would be possible to do?