[FEATURE] Multiple independent chat threads in Cowork Dispatch

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Currently, Dispatch only supports a single chat thread. When working on multiple unrelated tasks (e.g., researching a topic while managing files), all conversations pile into one thread. This causes the context window to fill up with unrelated information, degrading response quality and making it hard to maintain focused workflows.

Proposed Solution

Allow opening multiple independent chat threads within Dispatch, each with its own isolated context. A simple tab/sidebar UI would let users switch between threads without cross-contamination.

This would significantly improve productivity for users who juggle multiple parallel workstreams in Cowork.

Alternative Solutions

Restarting sessions loses all context. Opening multiple Claude Desktop instances doubles memory usage. Neither provides a seamless multi-thread experience within Dispatch.

Priority

High - Significant impact on productivity

Feature Category

Interactive mode (TUI)

Use Case Example

1. I ask Dispatch to research flight options for an upcoming trip
2. While that's running, I want to ask Dispatch to help organize files in my Downloads folder
3. Currently both tasks share the same thread, so flight research context mixes with file management context
4. With multiple threads, I could have "Travel planning" in one tab and "File cleanup" in another, each with clean, focused context

Additional Context

This is specifically about Cowork Dispatch (the persistent chat interface in Claude Desktop), not Claude Code CLI.