Codex asynchronous questions render as Markdown without answer controls

Codex's `request_user_input_async` emits an `agentMessage` with `delivery: "async"` and a structured `questions` array. VS Code's agent-host adapter maps that item to ordinary Markdown, so the question and suggested answers appear as text with no input controls.

Observed with VS Code 1.137.0 ARM64, commit `645f29cc3176500b4b5762ba887cf2a7f0ffdf2c`, connected to Ubuntu WSL with Codex 0.154.0. The same dispatcher from the original vendor server archive reproduces the failure, and current upstream source also lacks this mapping. This is independent of local feedback-review changes.

Reproduction: have a model supporting asynchronous questions call `request_user_input_async` with a question and two suggested answers. The native item contains structured questions, but the outgoing agent-host response is Markdown. Expected: selectable answers and a free-text entry, delivered without interrupting ongoing work and still answerable if native work completes first.

Proposed fix: #336512. It routes the structured event to the existing question carousel and handles completion, cancellation, delivery failure and RPC/event ordering. The focused source suite has 15 passing tests. Twelve bundle tests pass on the original/pre-install bundles; post-install checks pass with the two pre-install-only checks skipped. No full build or live UI validation is claimed.

[Source patch, installed-bundle backport and validation for PR #336512](https://github.com/RyanEwen/vscode-patches/blob/main/docs/patches/vscode-336512.md).

*AI disclosure: this comment and the related code were written with the assistance of AI.*