simple_chat: Agent appends onto text from a prior turn instead of adding new text at end of chat when responding to user

_↴ Ported from [flutter/genui#982](https://github.com/flutter/genui/issues/982) — originally opened by [andrewkolos](https://github.com/andrewkolos) on 2026-06-24._
_Original labels: front-line-handled_

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Reproduced on ffde58489f8e976288feb2ef4d6110515c58d269. Possibly related: https://github.com/flutter/genui/issues/517

Notice the part of the initial text starting with "Acknowledged!".

**Expected behavior**
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**Additional context**
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The issue is about a chat agent incorrectly appending to prior text instead of adding new text at the end. Start by examining the chat UI component and the state management for message history, likely in a file handling chat turns or agent responses. Look for the logic that concatenates or displays messages. The linked issue #517 may provide context. Test by reproducing the bug in the chat interface to see the 'Acknowledged!' text behavior.

Rédigé par le modèle d'indexation à partir du texte de l'issue.