Per-chat reasoning effort in contextual sheet

[YoussefKeyrouz]

Task/Issue URL: https://app.asana.com/1/137249556945/project/1212810093780571/task/1215062229903137?focus=true

Description

Wires the contextual Duck.ai sheet into the per-chat reasoning flow introduced by #8666 and fixes two correctness bugs

• Minor cleanup in ReasoningModePickerViewModel

Steps to test this PR

Per-chat scope restored on reopen

• Start a chat in the contextual sheet on tab A; pick a non-default model and reasoning effort; submit a prompt.
• Close the contextual sheet.
• Open new duck ai on another tab or submit a prompt via the native input field using a new model (global default changes)
• Reopen the contextual sheet on tab A (within the session window). Verify the picker reflects the reasoning effort, not the global default)
• Submit another prompt; confirm that the submission carries the chat's modelId and reasoningEffort.
• Open another tab and start a new chat in the contextual sheet on tab B
• Switching between tabs properly restore the reasoning effort of the corresponding chat.

Globals untouched

• After any per-chat submission above, dismiss the sheet and open Duck.ai from the address bar (or a fresh tab). Verify your global defaults are unchanged.

---

Note

Medium Risk
Moderate risk because it changes contextual sheet state management and how the native input widget resolves per-chat model/reasoning, which can affect prompt submission and session restore behavior.

Overview
Adds a chatId StateFlow to DuckChatContextualViewModel, extracted from the contextual webview URL and cleared on new-chat, so the UI can reliably identify the active chat across reopen/restore flows.

Wires that chatId into the contextual native input path by passing a chatIdFlow through DuckChatContextualFragment/ContextualNativeInputManager into NativeInputModeWidget.bindChatIdSource, enabling per-chat reasoning/model resolution in the native input picker. Includes a small correctness/cleanup tweak in ReasoningModePickerViewModel (single snapshot of modelState) and adds unit tests covering chatId lifecycle (initial, restore, page-load updates, and clearing).

^{Reviewed by Cursor Bugbot for commit 7159e2d. Bugbot is set up for automated code reviews on this repo. Configure here.}

[YoussefKeyrouz]

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

• Per-chat reasoning effort in contextual sheet #8674 👈 (View in Graphite)
• Per-chat model and reasoning restoration on existing Duck.ai chats. #8666
• Publish active chatId to NativeInputState (per-tab) #8664
• develop

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