Desktop app: top-level "+ New" always prompts for a folder (regression, no longer remembers last working directory)

## Description

In the Claude Code desktop app, clicking the top-level **"+ New"** now pops open a folder-selection dialog every time before I can type a prompt. Previously I could click "+ New" and immediately start asking questions, because the app reused my last-used working directory.

This is a regression in a recent desktop app update. It matches the now-closed/locked #46176 and #36175, which the auto-close bot asked users to re-file and reference.

## Expected behavior

Clicking "+ New" should reuse the last-used working directory (or a configurable default) and let me type a prompt immediately, with no folder picker.

## Current behavior

- Top-level "+ New" always opens a folder-selection dialog first.
- There is no per-project-group "New chat" button in my build, and the chat-header "⋮" menu (Artifacts, Files, Background tasks, Open in, Rename, Transcript view, Archive, Delete) has no "New chat" entry.
- So there is no way to start a new chat scoped to my project without re-selecting the folder each time.

## Suggested fix

Persist the last-used working directory across sessions, **or** add a `defaultWorkingDirectory` setting, **or** restore a "New chat" action on the project group / chat header that inherits the current folder.

## Environment

- Claude Code desktop app on Windows (WSL2 project directory)
- CLI works fine (inherits cwd from the terminal)

## Related

- #46176 (closed, locked)
- #36175 (closed, locked)

Start by reproducing the top-level "+ New" flow in the Claude Code desktop app on Windows with a WSL2 project directory, focusing on the folder-selection dialog and working-directory handling. Trace how the last-used directory is selected across sessions and compare it with the behavior described in #46176 and #36175. Done means "+ New" can reuse the last-used or configured directory and open directly for prompting without re-selection.

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