[FEATURE] Cowork scheduled tasks should be able to send feedback back to the parent session or inbox

Problem

Cowork scheduled tasks can run useful background workflows, but they do not appear to have a clean way to send structured feedback back to the parent session that created them.

This creates an awkward manual loop:

• the scheduled task discovers something important
• the task itself cannot hand that result back into the originating conversation
• the user has to manually open the parent session and copy the outcome back in

Example use case

A recurring scheduled task monitors some condition and reaches a conclusion that should influence the next step in the original conversation.

At that point, the ideal behavior is not necessarily to create another scheduled task. Often the right action is simply to send a concise result back to the parent session, or at least surface it in a dedicated inbox/notification stream tied to that workflow.

Expected behavior

Cowork scheduled tasks should have a supported way to return feedback to the workflow that spawned them, for example by allowing one or more of the following:

• send a summary/result to the parent session
• post to an inbox/notification feed associated with the parent workflow
• mark the parent session as needing attention with a short machine-generated summary

Why this matters

Without a return channel, scheduled tasks are much less useful for real office automation because they can observe and act, but they cannot cleanly hand results back into the main working context.

That forces unnecessary manual coordination even when the task already has exactly the information the user needs.

Suggested improvement

Add a safe, explicit return path from scheduled tasks to their parent context.

Even a constrained version would help a lot, for example:

• text-only summary back to the parent session
• bounded payload size
• no arbitrary tool execution in the parent, just a message/result handoff

Environment

• Cowork scheduled tasks
• Parent/child workflow created from a normal Cowork session