Add customize responses to native input

[joshliebe]

Task/Issue URL: https://app.asana.com/1/137249556945/project/1200204095367872/task/1215924137523437?focus=true
Tech Design URL (if applicable):

Description

• Adds a customize responses option to the native input when using Duck.ai

Steps to test this PR

• Start a chat
• Tap the option icon in the native input
• Tap “Customize Responses"
• Verify that the Customize Repsonses screen is opened
• Verify that the keyboard is hidden
• Dismiss the screen
• Verify that the keyboard is shown
• Verify that the option is only visible in Duck.ai

UI changes

Before	After

---

Note

Low Risk
Feature-flagged Duck.ai UI and JS bridge wiring with broad test coverage; no auth or data-path changes.

Overview
Adds Customize Responses to the Duck.ai native unified input options menu (only when input context is Duck.ai), with count/daily pixels and a submitCustomizeResponsesAction subscription so the web layer can open the customize screen.

The tap path runs OptionsView → NativeInputModeWidget → browser NativeInputCallbacks / BrowserTabViewModel.onCustomizeResponsesClicked(), matching other native menu actions.

Also adds a focusChatInput JS message that emits tab-scoped focusInputEvents (same pattern as model picker) so the FE can refocus the native field after dismissing customize UI. NativeInputModeWidget now observes those events and toggles the keyboard via InputMethodManager instead of Activity keyboard helpers when chat input is hidden/shown.

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[joshliebe]

• Add customize responses to native input #8958 👈 (View in Graphite)
• develop

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