[FEATURE] Cowork should display the active working folder persistently in the session UI

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

When working inside a Cowork session, there is no persistent visible indicator showing which folder is currently selected. Once a session is underway, there is no easy way to confirm which directory Claude is operating in without interrupting the workflow to ask directly.
This creates meaningful friction for users managing structured, multi-folder workspaces — particularly when switching between projects or tasks within a session. It is easy to lose track of which folder is active, and there is no reliable way to verify it without breaking focus.

Proposed Solution

Display the currently active working folder path visibly and persistently within the Cowork session UI — ideally in the header or sidebar — so users can confirm at a glance which directory Claude is operating in without having to ask or re-navigate.

Alternative Solutions

_No response_

Priority

High - Significant impact on productivity

Feature Category

File operations

Use Case Example

A knowledge worker managing multiple active project folders switches between tasks mid-session. Without a visible folder indicator, they have no way to confirm whether Claude is still operating in the correct directory, leading to uncertainty and the need to re-ask Claude to confirm its working context.

Additional Context

_No response_