Chrome integration: Support remote/SSH usage (Claude Code on VPS, Chrome on local machine)

Use Case

I'm running Claude Code on a remote VPS (accessed via SSH), but Google Chrome is installed on my local machine. The current Chrome integration architecture doesn't support this setup.

Current Limitation

The Chrome integration uses Chrome's Native Messaging API, which requires:

• Claude Code CLI and Chrome to be on the same physical machine
• Local communication only (no network-based communication)

This makes it impossible to use the Chrome integration when:

• Running Claude Code on a remote server via SSH
• Chrome is only available on the local workstation

Setup Details

[Local Machine]  ──SSH──>  [Remote VPS]
     ↑                          ↑
  Chrome here          Claude Code here

• VPS: Ubuntu Linux (SSH access only, no GUI)
• Local: Chrome installed and working
• Extension: Claude in Chrome 1.0.36+ installed locally

Requested Feature

Support for remote/SSH scenarios where Claude Code and Chrome are on different machines:

Option 1: Network-based communication

Allow the Chrome extension to communicate with Claude Code over a network connection (with proper authentication/security).

Option 2: SSH tunneling/forwarding

Provide a way to tunnel the Native Messaging communication through SSH, similar to X11 forwarding.

Option 3: Local proxy/bridge

A lightweight local bridge tool that runs alongside Chrome and forwards commands to the remote Claude Code instance.

Why This Matters

Many developers work in remote/cloud environments:

• Development servers in the cloud (AWS, DigitalOcean, OVH, etc.)
• Corporate VDI/remote desktop setups
• Docker/container-based development
• WSL users (though WSL is already documented as unsupported)

Being able to test web applications running on remote servers while keeping Chrome local would be extremely valuable.

Workarounds Considered

1. ❌ Run Claude Code locally: Not ideal for projects that must run on remote infrastructure
2. ❌ Install Chrome on VPS: Requires GUI, X server, poor performance over SSH
3. ✅ Current workaround: Disable --chrome flag and test manually

Related Issues

• Similar to #20298 (connection conflicts)
• Related to the architecture described in the docs: https://code.claude.com/docs/chrome

Request

Could you provide guidance on:

1. Whether remote/SSH support is planned for the Chrome integration?
2. Any recommended workarounds or architectural patterns?
3. Technical limitations that prevent this from working?

Thank you for considering this feature request!