[BUG] Double setup for name/role on web

### 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?

New users are asked to set up name/role twice during onboarding: once immediately after accepting an org invite (on claude.ai), and again on first run of Claude Code on the web. These two onboarding flows don't appear to check whether the profile step was already completed elsewhere.

### What Should Happen?

Profile info (name, role) entered during invite acceptance should carry over to Claude Code on the web, since both are under the same account/org. The setup step should be skipped if already completed.

### Error Messages/Logs

```shell

```

### Steps to Reproduce

Receive an org invite and accept it.
Complete the name/role setup prompt shown after accepting.
Navigate to Claude Code on the web (code.claude.com) for the first time.
Observe that the name/role setup prompt appears again.

### Claude Model

Sonnet (default)

### Is this a regression?

I don't know

### Last Working Version

_No response_

### Claude Code Version

N/A - web version

### Platform

Anthropic API

### Operating System

Windows

### Terminal/Shell

Other

### Additional Information

Claude Code on the web (code.claude.com)
First-time user, joined via org invite