Agents window temporarily duplicates submitted prompts in AHP-hosted sessions

Does this issue occur when all extensions are disabled?: Not tested; reproducing it requires an AHP-hosted session in the Agents window.

- VS Code Version: 1.134.0 (commit 110a328ea54b42367b803ec53ee0bf52ef26b419, 2026-08-18T18:24:44Z)
- OS Version: macOS 26.6.2, Darwin arm64 25.6.0
- Feature: Agents window with an AHP-hosted session

Steps to Reproduce:

1. Open an AHP-hosted session in the Agents window.
2. Enter a prompt and submit it.
3. While the agent turn is running, observe that the submitted prompt appears in its normal place in the conversation and also appears a second time at the bottom of the conversation.
4. Wait for the turn to finish. The second copy disappears when the turn completes.

Expected behavior:

The submitted prompt should be rendered once while the turn is running.

Actual behavior:

The Agents window temporarily renders the prompt twice. The second copy remains at the bottom while the turn is in progress, which makes it look as though the prompt was queued or submitted again. It disappears after the turn finishes.

This appears to be a UI/state issue rather than duplicate delivery to the hosted agent. It is distinct from #327586, where the same prompt was delivered to the agent twice after the first turn had completed.