[Vscode Agents] Need Speech-to-Text support in Agents window

### Problem
The new Agents window (opened via "Open in Agents window") doesn't load installed extensions, so the VS Code Speech extension isn't available there. In the regular Copilot Chat view I can install VS Code Speech and dictate my prompts, but that capability disappears the moment I switch to the Agents window.

Because the Agents window has no native speech-to-text either, the only way to interact with agents is by typing. For longer, more conversational agent prompts this is slow and tedious — dictation is exactly where it would help most.

### Expected behavior
I'd like to be able to use speech-to-text when talking to agents in the Agents window, either by:

Enabling the VS Code Speech extension (or its speech provider) inside the Agents window, or
Providing a native speech-to-text / dictation control in the Agents window chat input (a mic button consistent with the one in Copilot Chat).

### Actual behavior
Extensions (including VS Code Speech) are not enabled in the Agents window.
No mic / dictation button appears in the Agents window.
Agent interaction is type-only, which is slow for longer prompts.

### Why it matters
Speaking to an agent is far faster than typing for multi-sentence, exploratory prompts — which is the primary use case for agents. Parity with the speech input already available in Copilot Chat would make the Agents window meaningfully more usable.

### Environment
Extension: VS Code Speech (ms-vscode.vscode-speech)
VS Code version: `Version: 1.128.0
Commit: fc3def6774c76082adf699d366f31a557ce5573f
Date: 2026-07-07T15:14:24-07:00 (5 days ago)
Electron: 42.5.0
ElectronBuildId: 14525058
Chromium: 148.0.7778.271
Node.js: 24.17.0
V8: 14.8.178.33-electron.0
OS: Darwin arm64 25.5.0`

Start by tracing how the Agents window loads extensions and compare that path with the existing VS Code Speech integration in Copilot Chat. Determine whether speech input should be enabled through the extension or provided natively; done means agents accept speech-to-text through a mic control or equivalent supported flow.

Written by the indexing model from the issue text.