[BUG] [Cowork] Max plan: "New project" always creates an account-synced project, no way to create a local-only project

### Preflight Checklist

- [x] I have searched [existing issues](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20state%3Aopen%20label%3Abug) and this hasn't been reported yet
- [x] This is a single bug report (please file separate reports for different bugs)
- [x] I am using the latest version of Claude Code

### What's Wrong?

On a Max plan account, every project created via Projects > New project in Claude Desktop is saved to my Claude account and appears on claude.ai, even with Settings > Cowork > "Only on this computer" enabled.

The "New project" button opens a single dialog (name, goal, folder). The Folder field only binds a local folder on this machine ("Claude can work in this folder when you use the project from this computer"); the project itself is still created in the account.

The three creation options described in the help article "Organize your tasks with projects in Claude Cowork" (Start from scratch / Import a project / Use an existing folder) do not appear. That article states that projects created from a folder on your computer stay on that computer, but there is no longer a path to create one.

Existing local projects created before the July 2026 Chat/Cowork merge still work and remain local. Only new project creation is affected.

On a Team plan account, using the same app version on the same Mac, creating local projects still works.

### What Should Happen?

With "Only on this computer" enabled (or via an explicit option in the New project dialog), I should be able to create a new project whose metadata, instructions, sessions and memory are stored only on this computer and not synced to my Claude account, as documented.

### Error Messages/Logs

```shell

```

### Steps to Reproduce

1. Sign in to Claude Desktop with a Max plan account.
2. Settings > Cowork: enable "Only on this computer". Fully quit (Cmd+Q) and reopen.
3. Go to Projects and click "New project".
4. Enter a name, pick a local folder, click "Create project".
5. Open claude.ai in a browser with the same account and go to Projects.

Result: the new project appears on claude.ai (account-synced).
Expected: the project exists only on this computer.

### Claude Model

None

### Is this a regression?

Yes, this worked in a previous version

### Last Working Version

Unknown exact version; worked before the unified Projects UI shipped (around July 2026)

### Claude Code Version

Claude Desktop 1.49585.0 (41ad1d), built 2026-09-08 (Desktop app, not the Claude Code CLI)

### Platform

Anthropic API

### Operating System

macOS

### Terminal/Shell

Terminal.app (macOS)

### Additional Information

Environment:
- Claude Desktop version: 1.49585.0 (41ad1d), built 2026-09-08
- Platform: macOS 26.6.2 (25G83)
- Plan: Max (affected), Team (not affected, same app version)
- Settings > Cowork > "Only on this computer": enabled
- Terminal field not applicable: this is the Claude Desktop app UI, not the CLI

Local-only storage is a hard requirement for some of my work, so this blocks using Cowork projects for it on my personal account.

A support ticket has also been filed with Anthropic support.

Related: #67330 (references the previous "Start from scratch" / "Choose project location" flow), #62194 (notes the Cowork project catalog was previously local-only).

Begin with Claude Desktop's Projects > New project flow after enabling Settings > Cowork > Only on this computer, using the reported Max-plan reproduction steps. Compare the creation behavior with the Team-plan case and the documented local-project flow. Done means a Max-plan user can create a project whose metadata, instructions, sessions, and memory remain on the computer and do not appear on claude.ai.

由索引模型根据 Issue 内容生成。