Project-scoped CDP browsers for agents: link routing and parallel browser contexts

Describe the Bug

I use Cursor with project-specific Chrome instances connected through CDP.

This is useful when browser work needs to stay inside one project context: its own tabs, cookies, notes, task state, and agent conversation.

The current gap is link routing. When an agent writes a URL, clicking it can open the system browser or Cursor Browser Tab. That breaks the workflow because those are separate browser sessions with different state.

I would like each agent session to have an explicit browser target:

Cursor Browser Tab
default external browser
an attached CDP browser instance
If an agent session is attached to a CDP browser, links from that session should open there, ideally in a new tab.

I also think browser contexts should be isolated and usable in parallel. I tested two separate CDP browser instances successfully, but I have not tested higher concurrency. A clear supported model for multiple agents and multiple isolated browser contexts would help avoid conflicts between projects, accounts, and tasks.

This would be useful beyond software development. For example, a person could use Cursor to research travel options, compare information from web services, prepare content, or work through an English-speaking forum while keeping each project isolated.

In my case, Cursor helps overcome a language barrier. I speak Russian, but I can research, draft messages, and participate in English discussions while keeping the browser and project context together.

Browser automation should still keep clear safety boundaries: isolated profiles, visible active browser target, explicit approval before external actions, and no silent switching to another browser session.

I have worked with browser automation for a long time and would be happy to test or share practical feedback about profile isolation, parallel runs, approvals, and failure cases.

Steps to Reproduce

123

Screenshots / Screen Recordings

Operating System

Windows 10/11

Version Information

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Does this stop you from using Cursor

No - Cursor works, but with this issue