DuckAi/Sidebar: Implement replace Chat Sidebar with chats history

[karlenDimla]

Task/Issue URL: https://app.asana.com/1/137249556945/task/1218228567702514?focus=true
Tech Design URL (if applicable):
API Proposals URL(s) (if applicable):

Description

Steps to test this PR

Feature 1

• [ ]
• [ ]

UI changes

Before	After
!(Upload before screenshot)	(Upload after screenshot)

---

Note

Medium Risk
Changes Duck.ai omnibar navigation behind a feature flag with legacy fallback, but wrong-flag behavior would affect a high-traffic entry point.

Overview
Adds a nativeDuckAiSidebar feature flag (remote toggle, default internal) and wires omnibar sidebar taps through onDuckChatSidebarButtonPressed(). When the flag is on, the button opens native chat history (openDuckChatHistory() / LaunchDuckChatHistory when available); when off, behavior stays on the legacy web sidebar via NativeAction.SIDEBAR.

Also corrects swapped JS bridge actions so openDuckChatSidebar() emits SIDEBAR and onCustomizeResponsesClicked() emits CUSTOMIZE_RESPONSES. Unit tests were updated for customize responses, sidebar/history fallbacks, and the new flag branch.

^{Reviewed by Cursor Bugbot for commit 6c82012. Bugbot is set up for automated code reviews on this repo. Configure here.}

[karlenDimla]

• DuckAi/ChatTab: Add New Image, New search and remove New Tab option from + menu  #9761
• Duck.Ai/ChatHistory: Add context menu #9760
• DuckAi/Sidebar: Implement replace Chat Sidebar with chats history #9752 👈 (View in Graphite)
• develop

This stack of pull requests is managed by Graphite. Learn more about stacking.

[github-actions]

⚠️ API Proposal reminder

This PR changes the public surface of one or more -api modules, but the API Proposals field of the PR description is empty. This is a non-blocking reminder — please double-check whether a proposal is needed.

Changed -api source files:

• duckchat/duckchat-api/src/main/java/com/duckduckgo/duckchat/api/DuckAiFeatureState.kt

To clear this reminder, edit the PR description and either:

• add the approved API Proposal link(s) in the API Proposals field (one per line), or
• write None there if this PR does not change the public API (e.g. KDoc, comments, tests).

See the API Proposals section in .claude/docs/contributions.md for details.