Chrome extension permissions trigger locally instead of through SSH tunnel

Description

When running Claude CLI through a remote SSH session (e.g., VS Code Remote SSH), the Claude in Chrome extension's permission prompts and interaction steps are triggered on the local machine rather than being routed through the SSH tunnel to the remote CLI session.

Scenario

1. User connects to remote server via SSH tunnel (e.g., VS Code Remote SSH)
2. User runs Claude CLI on the remote server
3. User attempts to use Chrome browser automation tools (mcp__claude-in-chrome__*)
4. Permission dialogs and required interaction steps appear on the local machine
5. The remote CLI session doesn't receive the responses/cannot proceed

Expected Behavior

When using Claude CLI through an SSH tunnel with the Chrome extension:

• Permission prompts should be routed back to the remote CLI session
• The extension should detect it's being controlled from a remote session
• User interaction steps should be synchronized between local Chrome and remote CLI

Current Behavior

• Permissions get triggered on local machine
• Remote CLI session hangs waiting for responses that never arrive
• No indication to the user that there's a mismatch between local/remote contexts

Environment

• Claude CLI running on: Remote Linux server via SSH
• Chrome extension running on: Local machine
• Connection method: VS Code Remote SSH / SSH tunnel
• Claude CLI version: 2.1.17
• Extension: Claude in Chrome (Beta)

Suggested Improvements

1. Detect when CLI is running in a remote/SSH context
2. Provide clear error messaging about local/remote mismatch
3. Consider WebSocket or tunnel-aware communication between extension and CLI
4. Document limitations when using Chrome extension with remote sessions