#2759 Add a single-file chat HUD

Description

## Title

Add a single-file chat HUD

Issue: none

## Summary

Chat and the live monitor share one page. Saved chats are a two-level tree, and a thread can be dragged onto the prompt to attach it.

The change is one HTML file. Copy `strata-chat-hud.html` over `serve/web/index.html`. `GET /` already serves that path, so the server does not need a code change. The four composer icons use the existing `serve/web/sprite.svg`.

## What changed

- Add `strata-chat-hud.html`.
- One screen: live figures, context, and the machine sit in the side panel next to the chat. History is the other tab of that panel.
- History: folders and threads, two levels deep. New threads appear at the top and can be dragged into a folder. A folder that already has children cannot be nested again. The tree is stored in this browser's localStorage.
- Drag a thread onto the prompt to attach it. The transcript sits above the prompt as a file card and goes out with the next message.

## Extra Notes

- Chat, metrics, and Unload use the existing server endpoints.
- The Load button's model list calls a local helper that is not in this PR. Without it, that list does not load. The screen, the history tree, and the drag do not need it.
- Nunito and JetBrains Mono are requested from Google Fonts. Segoe UI and Consolas are the fallbacks.