[FEATURE] Cowork: respect ANTHROPIC_BASE_URL / support corporate API gateways

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

My workplace has an approved provider pipeline (portkey.ai) which is working great for claude code, but doesn't seem to be supported (yet) by cowork.

Proposed Solution

Respect the same environment variables that claude code does:

• ANTHROPIC_BASE_URL
• ANTHROPIC_AUTH_TOKEN
• ANTHROPIC_CUSTOM_HEADERS

Alternative Solutions

_No response_

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_