[FEATURE] Add voice conversation mode to Dispatch — talk to Claude, not type to it

Feature request

Add a real-time voice conversation mode to the Dispatch UI on iOS (and ideally desktop). Right now Dispatch is a text-message-style interface — type, hit send, wait for text reply. Voice conversation would let users speak to Claude and hear responses back, like a phone call.

Why this matters

For users on iPad-only / accessibility / hands-free workflows, the current "type-and-tap" model is high-friction. A voice mode (similar to ChatGPT's Voice Mode or Gemini Live) would unlock:

• Long-form planning conversations — verbalize ideas, get pushback, iterate fast
• Workflow operation while away from keyboard — driving, lying back, walking, recovering from injury (literal use case for me right now)
• Accessibility — users who can't type comfortably (RSI, mobility, vision)
• Speed — speaking is 3-4x faster than typing

Proposed UX

• Toggle in Dispatch header: "Voice Mode"
• Tap → switches to fullscreen voice UI with waveform indicator
• Claude speaks responses out loud while continuing to use sub-tasks/tools in the background
• Visual log of the conversation shown below the waveform for reference
• Tap to interrupt mid-response (like ChatGPT)
• Auto-detect speaker silence to commit each turn (no manual "send")
• Optional speech-to-text fallback for review/editing

Existing reference points

• ChatGPT Voice Mode — Standard + Advanced (real-time, low-latency)
• Gemini Live — full duplex, can interrupt
• Claude Voice Mode (web) — Anthropic already shipped this for claude.ai chat per support article 11101966; just not in iOS Dispatch

Severity / impact

For some users this is the difference between "I can use Claude as my CTO" and "I can't realistically work with Claude today." Voice unlocks AI as a true working partner for non-keyboard contexts.

Related issues

• #32597 — Voice input not available in Dispatch
• #36581 — Voice/microphone for Code web interface
• #30808 — Mic icon in chat input

This is the bigger ask those bugs hint at. Even a tap-to-talk mode (no full duplex) would be a major win.