"+ New" doesn't prompt for a project folder — easy to start a session in the wrong project

### Preflight Checklist

- [x] I have searched [existing requests](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20label%3Aenhancement) and this feature hasn't been requested yet
- [x] This is a single feature request (not multiple features)

### Problem Statement

When starting a new session via the "+ New" button, there's no upfront prompt to choose which project folder the session should use. The folder/project selector is a small button tucked at the bottom of the screen (next to "Local" and the git branch indicator), easy to miss if you don't already know it's there.

As a result, it's easy to click "+ New" expecting to start a fresh session for a different project, only to realize afterward that you were still working inside whatever folder the previous session was pointed at.

### Proposed Solution

Suggestion: When a user clicks "+ New," prompt them to pick or confirm the project folder as the first step (or at least surface the current folder much more prominently), rather than requiring them to notice and click the small folder button at the bottom of the screen after the fact.

### Alternative Solutions

_No response_

### Priority

Critical - Blocking my work

### Feature Category

CLI commands and flags

### Use Case Example

_No response_

### Additional Context

_No response_

No implementation files, tests, or entry points are named. Start by tracing the "+ New" flow and the existing project-folder selector near the Local and git branch indicators. Done means a new session prompts for or clearly confirms its project folder before work begins.

Written by the indexing model from the issue text.