[FEATURE] Watch folder integration for Chat projects with Cowork file synchronization

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 using Claude Chat projects alongside Cowork, the two tools operate in isolated contexts. I want to use Chat to maintain analytical context and decision-making around a project (e.g., financial planning) while simultaneously having Cowork autonomously handle file organization and batch processing on related files.
Currently, this workflow requires:

Manually checking Cowork's outputs and copying them into Chat
Maintaining parallel context systems between tools
Losing continuity as files change without the Chat project knowing

Proposed Solution

Add a watch folder feature to Claude Chat projects that:

Allows designating a specific folder to monitor
Automatically detects file changes made by Cowork
Makes updated/new files available as context within the Chat project
Enables seamless conversation about files that are actively being modified by Cowork

Alternative Solutions

Currently, I'm working around this by:

Manually checking Cowork's output folder periodically and copying/pasting results into Chat
Creating summary files that Cowork generates, which I then reference in Chat
Maintaining separate context documentation in each tool to keep them loosely synchronized

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

I maintain a financial planning Chat project with analysis and strategy context. Meanwhile, Cowork organizes supporting documents, creates summaries, and batch-processes receipts in a designated folder. With a watched folder, Chat would automatically see these updates and I could reference them in conversation without manual handoffs.

Additional Context

_No response_