[BUG] HTTP_PROXY/HTTPS_PROXY not respected when using apiKeyHelper configuration

Environment

• Claude CLI version: @anthropic-ai/claude-code: 1.0.34
• Operating System: macOS 15.5
• Terminal: Terminal App

Bug Description

HTTP_PROXY and HTTPS_PROXY environment variables are not respected when using apiKeyHelper configuration, preventing proxy routing of inference requests.

Steps to Reproduce

1. Set HTTP_PROXY and HTTPS_PROXY environment variables
2. Configure Claude Code with apiKeyHelper in ~/.claude/config.json
3. Execute Claude Code commands that make inference requests
4. Monitor proxy logs for traffic

Expected Behavior

All Claude Code network requests (including inference requests) should route through the configured proxy when HTTP_PROXY/HTTPS_PROXY are set.

Actual Behavior

• Telemetry requests route through proxy correctly
• Inference requests aren't route through proxy when apiKeyHelper is configured
• Removing apiKeyHelper allows inference requests to use proxy

Additional Context

Issue only occurs with apiKeyHelper configuration. When using direct ANTHROPIC_API_KEY environment variable instead of apiKeyHelper, proxy routing works as expected for inference requests.