[Bug] Chrome MCP tools fail with "modelApiKey is required" despite authenticated CLI and connected extension

Bug Description

The Claude in Chrome MCP server shows as connected (green checkmark in /status), but when actually invoking any chrome browser tools, they fail with the error:
{"error":{"message":"modelApiKey is required"}}

The CLI is fully authenticated with a Claude Max subscription, and the Chrome extension works fine when used standalone in the browser sidebar. The issue only occurs when Claude Code tries to use the MCP tools to control the browser.

Environment Info

• Platform: darwin (macOS)
• Claude Code Version: 2.0.76
• Login method: Claude Account
• MCP servers: claude-in-chrome shows connected with green checkmark

Steps to Reproduce

1. Authenticate Claude Code with Claude Max subscription (/login)
2. Install Claude in Chrome extension and log in via browser
3. Run claude --chrome or enable chrome via /chrome
4. Verify /status shows claude-in-chrome MCP server connected
5. Ask Claude to use any chrome tool (e.g., "navigate to localhost:3000")
6. Observe error: {"error":{"message":"modelApiKey is required"}}

Expected Behavior

Chrome browser tools should work using the authenticated Claude Max subscription, same as all other Claude Code functionality.

Actual Behavior

MCP connection appears successful, but tool invocations return modelApiKey is required error, suggesting the extension expects a separate API key configuration that doesn't exist in the UI.

Additional Context

• The Chrome extension sidebar works perfectly when used directly in the browser
• This appears to be an authentication handoff issue between Claude Code CLI auth and the Chrome extension's MCP integration
• There is no visible place in the Chrome extension settings to configure a "modelApiKey"