Feature Request: Support external browser password autofill in integrated browser

**Describe the feature**

When using the [integrated browser](https://code.visualstudio.com/docs/debugtest/integrated-browser) in VS Code to access login pages (e.g., GitHub OAuth for Copilot sign-in, extension auth), saved passwords from Microsoft Edge (or other system password managers like Windows Credential Manager) cannot be auto-filled.

In Microsoft Edge, when visiting a login page, the browser offers to automatically fill in saved credentials with a single click. VS Code's integrated browser, despite being Chromium-based (Electron), does not integrate with the system's password manager or browser extensions to provide this functionality.

**Steps to reproduce**

1. Save a password for a website (e.g., github.com) in Microsoft Edge
2. Open VS Code and trigger a flow that opens the integated browser to the same login page
3. Observe that no password autofill prompt appears

**Expected behavior**

The integrated browser should be able to access and auto-fill credentials saved in the system's default browser or OS credential manager, similar to how a regular browser tab works.

**Current workaround**

Users have to manually type their credentials each time they need to sign in in the integrated browser, or copy-paste from an external password manager window.

**Impact**

This affects all authentication flows that use VS Code's integrated browser, including:
- GitHub authentication for Copilot
- MCP server OAuth setup
- Extension authentication (Azure, etc.)
- Settings Sync sign-in

**Related**

- #300149 (HTTP Basic Auth support for integrated browser)
- This is a known limitation of Electron's webview/BrowserView — it runs in an isolated context without access to the host system's browser profile or password manager.