[BUG] VS code extension doesn't allow use API key without signing in

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report (please file separate reports for different bugs)
• [x] I am using the latest version of Claude Code

What's Wrong?

Where was an issue #441 about using API code without login.
It has comments how to skip login screen for console claude code. However, VS code extension still shows login screen.

What Should Happen?

VS code extension should accept API key without login or read API configuration similar to CLI claude code

Error Messages/Logs

Steps to Reproduce

Open VS code extension
Try to use API key without login

Claude Model

None

Is this a regression?

Yes, this worked in a previous version

Last Working Version

_No response_

Claude Code Version

2.0.27 (Claude Code)

Platform

Anthropic API

Operating System

Windows

Terminal/Shell

VS Code integrated terminal

Additional Information

_No response_