cant sign in in vs code never opens browser

Title: Amazon Q and AWS Toolkit auth commands do nothing in VS Code on Windows; Q hangs on "Authenticating in browser..." and no browser prompt appears

## Problem

On Windows, Amazon Q in VS Code gets stuck on `Authenticating in browser...` and never opens a browser.

At the same time, AWS Toolkit auth commands also appear broken:
- `Connect to AWS`
- `AWS: Add New Connection`
- other AWS auth/connection commands

They either do nothing or never open the AWS auth UI.

A key symptom is that VS Code never shows its normal external-link prompt (`Do you want to open this link in browser?`) during the Amazon Q / AWS Toolkit sign-in flow.

## Expected behavior

After entering the IAM Identity Center start URL and region, VS Code should hand off to the browser and complete sign-in.

## Actual behavior

Amazon Q shows:
- `Authenticating in browser...`

and stays there forever.

No browser opens.
No VS Code browser prompt appears.

AWS Toolkit auth commands also do not seem to execute normally.

## Environment

- OS: Windows 11
- VS Code version: 1.116.0
- Amazon Q extension version: 2.0.0
- AWS Toolkit extension version: 4.1.0
- AWS CLI version: 2.33.17

## Repro steps

1. Open VS Code.
2. Open Amazon Q.
3. Choose `Company account`.
4. Enter IAM Identity Center Start URL and region.
5. Click `Continue`.

## Result

The view changes to `Authenticating in browser...` and never progresses.

Also, AWS Toolkit commands like `Connect to AWS` / `AWS: Add New Connection` do not launch the auth flow.

## Important observations

- Normal external links in VS Code do work.
- Example: a plain `https://example.com` link can open successfully.
- This suggests the general VS Code/browser integration is working, but the AWS auth handoff is failing before it reaches the normal browser-open step.

## Additional troubleshooting already tried

- Reinstalled VS Code
- Wiped VS Code user data/settings/extensions and started fresh
- Reinstalled Amazon Q
- Installed AWS Toolkit separately
- Disabled all other extensions
- Tested with only Amazon Q enabled
- Tested with AWS Toolkit installed afterward
- Removed Copilot Chat interference
- Verified normal browser links can open from VS Code
- Successfully authenticated outside VS Code with AWS CLI

## External auth succeeds outside VS Code

This worked successfully in PowerShell:

```powershell
aws login --profile default --remote

The issue names no source files or tests. Start by reproducing the Amazon Q and AWS Toolkit authentication commands on Windows 11, then trace the handoff after the IAM Identity Center URL and region are submitted; done means the browser prompt or browser opens and sign-in completes instead of remaining on “Authenticating in browser...”.

Written by the indexing model from the issue text.