feat(github-cli): support private extension installs

[Tyler Kropiewnicki (tylerkrop)]

• Support installing private extensions with  GH_TOKEN/GITHUB_TOKEN
• Forward authentication to the selected non-root user and use gh auth git-credential for cloning
• Prevent temporary build authentication from incorrectly disabling the extension-list fallback

Testing

• Passed the existing public extension scenario
• Built with a private repository using a BuildKit secret and verified the token was not persisted in the image

[Tyler Kropiewnicki (tylerkrop)]

@microsoft-github-policy-service agree company="GitHub"