[FEATURE] Full two-way voice mode (speech in and out) for Cowork

### Preflight Checklist

- [x] I have searched [existing requests](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20label%3Aenhancement) and this feature hasn't been requested yet
- [x] This is a single feature request (not multiple features)

### Problem Statement

Cowork currently only supports dictation, speech to text input. There is no hands free, two way voice conversation like the voice mode already available in Claude's regular mobile, desktop, and web chat apps.

This makes Cowork hard to use while multitasking or away from the keyboard and screen, for example while walking, commuting, or doing other work, where typing a prompt and reading a long response back is impractical.

### Proposed Solution

Bring the same two way voice mode already in Claude's regular chat apps into Cowork. Let the user speak their request and have Claude's replies read back audibly, with a toggle similar to the existing sound wave icon in the regular chat apps, so a Cowork task can be run and monitored fully hands free.

This is a separate request from issue #64347, which asked only for text to speech output. This request is for full two way voice (speech in and speech out, hands free).

### Alternative Solutions

_No response_

### Priority

Medium - Would be very helpful

### Feature Category

Interactive mode (TUI)

### Use Case Example

_No response_

### Additional Context

_No response_

No files, tests, or entry points are named. Start by locating Cowork's interactive TUI and its existing dictation speech-to-text handling, then compare the voice-mode behavior in Claude's regular chat apps. Done means Cowork supports hands-free speech input and audible Claude replies behind a toggle similar to the existing sound-wave control.

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