[FEATURE] Dispatch/Cowork should have visibility into all Claude Code sessions, not just self-spawned ones

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

In Cowork/Dispatch mode, list_sessions and read_transcript only return sessions that Dispatch itself spawned via start_task or start_code_task. Sessions that the user manually opened in the Claude Code tab are completely invisible to Dispatch.

This creates a fragmented experience: when a user asks Dispatch "how's that Code task going?", Dispatch cannot find it if the user started it manually in the Code tab. Dispatch is positioned as the central orchestrator with a full view of all ongoing work, but in practice it only has partial visibility.

Real scenario: User had a long-running Claude Code session processing data files. They asked Dispatch to check on its progress. Dispatch could not find the session in list_sessions and had to ask the user to check manually — defeating the purpose of having a central coordinator.

Proposed Solution

list_sessions should return ALL active sessions across the Claude desktop app, including:

• Sessions spawned by Dispatch (start_task, start_code_task)
• Sessions the user manually opened in the Code tab
• Sessions from other Cowork conversations

Each session should include a field indicating its origin (e.g., source: "dispatch", source: "code_tab", source: "other_cowork").

read_transcript should work on any session ID returned by list_sessions, regardless of origin. At minimum, Dispatch should be able to read status (running/idle) and recent transcript. send_message access to non-self-spawned sessions could be optional or require user confirmation.

Alternative Solutions

Currently the user has to manually check the Code tab for session status and relay the information back to Dispatch, which is cumbersome and defeats the purpose of a central orchestrator.

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

1. User starts a long-running code task directly in the Code tab (e.g., data processing, refactoring)
2. User switches to Cowork/Dispatch and asks "how's that task going?"
3. Dispatch should be able to find and report on the task's progress
4. Currently Dispatch cannot see the task at all and has to ask the user to check manually

Additional Context

_No response_