AWS sign in screen is blank - can't log in

## Problem

## Steps to reproduce the issue

1. Choose 'personal account' for sign in.
2. Click on 'Open on external website'
3. See blank screen

## Expected behavior

See a login screen

## System details (run `AWS: About` and/or `Amazon Q: About`)

- OS: Mac Sequoia
- Visual Studio Code version: 1.105
- AWS Toolkit version:
- Amazon Q version: 1.106

Start by reproducing the sign-in flow: choose “personal account,” click “Open on external website,” and compare the blank screen with the expected login screen. Check the reported OS, Visual Studio Code version, and Amazon Q version using the listed “AWS: About” or “Amazon Q: About” entry points; done means the external sign-in page displays and allows login.

Written by the indexing model from the issue text.