[FEATURE] Cowork browser tasks should run in background / separate Chrome instance

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

Summary
When Cowork uses the browser to complete tasks, it takes focus away from
the user's active Chrome window. There should be an option to run browser
tasks in a background or separate Chrome instance.

Current behavior
Cowork uses the Claude in Chrome extension in the user's active browser,
which steals window/tab focus during task execution.

Proposed Solution

Desired behavior

• Option to run Cowork browser tasks in a separate Chrome profile or window

that stays in the background

• Or support for a dedicated "Cowork browser" instance that doesn't interfere

with the user's active browsing session

Why this matters
Users often want to assign Cowork a browser-based task and continue working
in their browser uninterrupted. Focus stealing makes it difficult to use the
computer normally while Cowork is running.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_