Automated worktree creation for chats in projects

### Before filing

- [x] I searched [open and closed issues](https://github.com/block/berd/issues?q=is%3Aissue) for duplicates.
- [x] I am using a recent [release](https://github.com/block/berd/releases) and this doesn't already exist.
- [x] This is one request, not several bundled together.

### Closest existing issue

none

### Is this new, or an improvement?

Improvement — Berd does this, but badly

### The problem, in your terms

Absolutely love your new Cursed thing. This is something we dreamt about for a while while I was still at Block, and then I'm happy to see it came to fruition, but this one gap behind the modern harnesses is killing me.

When I'm working in Codex or Claude Code, I have my "Create new worktree" checkbox always checked. It creates a worktree for every chat, and it doesn't interfere with one another. This is missing here at berd, and I would very much love to use it when this is gonna be a thing.
For now, I'm essentially blocked because creating a work tree every time manually is annoying.

### What you do today

waiting)

### What you'd like to see

Checkbox for automatically generated work trees when you start a new chat

### Why this belongs in Berd itself

Part of UI and the core functionality

### Non-goals

I'm not asking to utilize the native Worktree functionality of clients if it's very hard, and just asking for a way. It could be just the right Git creation and then giving them the folder.

### Alternatives you considered

_No response_

### Mockups, prior art, or other context

_No response_

Start at the new-chat UI and inspect the existing worktree handling in Berd's core functionality. Trace how a chat receives its working folder and identify the available Git worktree entry point. Done means a checkbox can enable automatic worktree creation for each new chat, with chats isolated from one another.

Written by the indexing model from the issue text.