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 |

未指定任何 repository 文件或测试。从 Settings > Gateway > Remote Connection 提案和 /chat 入口点开始，然后梳理 headless daemon、URL、session token 和 WebSocket 连接如何覆盖 parsing、tool execution 和 caching。完成的标准是达成一致的 remote gateway 设计，并实现 thin client 的端到端工作流。

由索引模型根据 Issue 内容生成。