[FEATURE] Allow `apiKeyHelper` to set the `ANTHROPIC_BASE_URL` used

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When developing apiKeyHelper in an enterprise, it's necessary to point ANTHROPIC_BASE_URL to the non-production environment.
However, these settings (apiKeyHelper and ANTHROPIC_BASE_URL) are set in managed-settings.json.

This means even though I can change the key returned by the helper to the dev environment, I can't test this and configure claude to use the dev ANTHROPIC_BASE_URL.

Proposed Solution

1. Allow the apiKeyHelper to set the environment environment variables for claude

or

1. Allow these other fields to use helpers

or

1. Something like: https://github.com/anthropics/claude-code/issues/4276

Alternative Solutions

I have to uninstall the managed settings (which is a hassle since it's MDM managed) just to test the changes in dev.

Priority

High - Significant impact on productivity

Feature Category

Configuration and settings

Use Case Example

_No response_

Additional Context

_No response_