[FEATURE] Dispatch: attach to existing cowork sessions instead of always spawning new 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

Dispatch currently spawns a new Cowork session for every task sent from mobile. There is no way to continue, monitor, or interact with an existing Cowork task that was started on the desktop.

This means if I start a complex, multi-step task at my desk and then leave, I can't pick it up from my phone. I have to wait until I'm back at my computer, or start the whole thing again from scratch via Dispatch, which creates a duplicate session with none of the prior context.
The core value of Dispatch is "fire a task, walk away, come back to finished work." But that only works for tasks short enough to complete unattended. Anything that needs steering, clarification, or a follow-up prompt mid-flight is locked to the desktop.

NB: Acknowledging the claude-code repo, however it is my understanding that claude cowork is a gui wrapper and the session routing would need to be solved here.

Proposed Solution

Let Dispatch attach to an existing active Cowork session rather than always creating a new one. This could work as:

• Session picker on mobile — When opening Dispatch, show a list of active Cowork sessions (title, status, last activity). Tapping one opens a mobile view of that session's conversation thread where I can read progress and send follow-up messages.
• Continue vs. new task — Keep the current "send a new task" flow as the default, but add a way to switch into an existing session. Could be as simple as a "Continue active task" option above the message input.
• Read-only as a minimum — Even if bi-directional interaction with an existing session is hard, read-only access to active Cowork task progress from mobile would cover the most common case: checking whether something finished, reading output, and deciding whether to intervene when back at the desk.

Alternative Solutions

1. Using an OpenClaw (or similar)
2. Starting the cowork task via dispatch on mobile app (every single time) is frustrating.

Priority

High - Significant impact on productivity

Feature Category

Other

Use Case Example

1. Start cowork task on desktop
2. Leave to commute / travel
3. Continue cowork task on mobile app

Additional Context

Issue #37713 addresses Dispatch session isolation from Projects (no shared context, directory access, or file presentation permissions). That's about the spawned session lacking inherited context.
This request is about session routing: the ability to connect Dispatch to an already-running session rather than always creating a new one.