Feature request: remote gateway mode to offload processing to a separate machine

## What

I'd like a way to run the my Copilot sessions on a remote machine and connect the desktop app to it as a thin client.

## Why

I use a low-spec portable laptop. The desktop app eats my RAM and CPU doing workspace parsing and background orchestration that could easily run somewhere else. VS Code Remote Tunnels solve this for editing, but they don't help with the standalone Copilot app's own resource usage — the app still does everything locally.

I looked at how [Hermes](https://github.com/fathah/hermes-desktop) handles this. They let you run `hermes dashboard --host 0.0.0.0 --port 9119` on a remote box and connect a lightweight client to it. The separation works well in practice.

## Proposed solution

Add a **Settings > Gateway > Remote Connection** panel where I can point the app at a remote server running a headless Copilot daemon. The desktop app would only handle rendering and input; everything else streams over WebSocket to the remote machine.

Roughly:
1. Let users spin up a headless copilot process on a server/VM/homelab
2. Connect from the desktop app with a URL + session token
3. All parsing, tool execution, and caching happens on the remote side

This would help anyone on a thin client, a locked-down enterprise laptop, or just a machine that throttles under load.

| Field | Value |
|-------|-------|
| App version | 1.0.25 |
| OS | Windows 10.0.26200 |
| Theme | GitHub |
| Path | /chat |
| Tenure | Day 1 |

No repository files or tests are named. Start at the Settings > Gateway > Remote Connection proposal and the /chat entry point, then map how a headless daemon, URL, session token, and WebSocket connection could cover parsing, tool execution, and caching. Done would require an agreed remote gateway design and an end-to-end thin-client workflow.

索引モデルが issue の本文から書いたものです。