Fix native input stop button bug

[joshliebe]

Task/Issue URL: https://app.asana.com/1/137249556945/project/1200204095367872/task/1215778085975943?focus=true
Tech Design URL (if applicable):

Description

• Hides the stop button in the native input in browser mode

Steps to test this PR

• Type a prompt (e.g. “generate a long essay about ducks”)
• While it is still generating, go back
• Verify that the stop button is not visible in the browser native input

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Note

Low Risk
Small UI visibility change in one ViewModel with dedicated tests; no auth, data, or API changes.

Overview
Fixes the native input stop streaming control appearing when it should not: visibility now requires active chat streaming and a non-browser InputContext (DUCK_AI or DUCK_AI_CONTEXTUAL), so browser/search native input no longer shows stop while a streaming flag may still be set.

Adds StopStreamingViewModelTest covering Duck AI visibility, suppression in BROWSER while streaming, non-streaming cases, and hiding when context switches to browser mid-stream.

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[joshliebe]

• Fix native input stop button bug #8907 👈 (View in Graphite)
• develop

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