Stuck on "Signing in to github.com..." in VS Code

### Describe the bug.

When trying to sign in to GitHub in VS Code, the process gets stuck on "Signing in to github.com..." and does not complete.

The browser may open, but VS Code does not finish authentication. The login process hangs and I cannot use GitHub features inside VS Code.

### Please attach log file(s) here if you have any.

The log file location should be copied to your clipboard if you came from VS Code.

### Reproduction Steps

1. Open VS Code
2. Click on "Sign in to GitHub"
3. Browser opens for authentication
4. Approve access
5. VS Code shows "Signing in to github.com..." and does not complete

### Expected Behavior

VS Code should successfully authenticate and complete the sign-in process.

### Exceptions & Errors (if any)

No error message displayed. VS Code just stays on the signing in screen.

### .NET Install Tool Version

v2.1.3

### Your operating system? Please provide more detail, such as the version and or distro above.

N/A

### VS Code Version

Windows 11 23H2 (64-bit)