Use `open_browser_page` tool from VSCode Copilot Chat

### Describe the feature or problem you'd like to solve

Copilot Chat cannot currently open and drive a browser without external support.

### Proposed solution

Allow Copilot Chat to open and control a browser in a connected VS Code instance.

### Example prompts or workflows

```
Browse my local development environment hosted at localhost:3000 to test the changes in the previous commit.
```

```
Follow these steps from the company knowledge base against the development instance of the app.
```

```
Navigate to this page and take a screenshot. Then, check out this branch and repeat.
```

### Additional context

There are several editor-agnostic ways to control a browser right now, including playwright-mcp and playwright-cli. However, I haven't found those to be quite as effective as the VSCode integrated browser. The integrated browser also includes some security features such as isolated sessions, which bring some peace of mind.

This feature is important enough to me that it's the only reason I continue to use VSCode Copilot Chat. I find myself hopping between Autopilot in Copilot CLI in a sandboxed dev container and VSCode Copilot Chat in a local folder. I will only jump out to the latter if I need to use the browser.

Start by tracing the existing open_browser_page tool and the integration boundary between Copilot CLI and VS Code Copilot Chat. Define how a connected VS Code browser would be opened and controlled, including localhost navigation, knowledge-base workflows, branch comparisons, and screenshots. Done means Copilot Chat can perform those browser workflows through the connected VS Code instance.

Written by the indexing model from the issue text.