[BUG] defaultMode: "plan" setting not applied when using `/clear` command

Preflight Checklist

• [x] I have searched existing issues 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?

When defaultMode is set to "plan" in the global settings file, new conversations started via the /clear command do not enter plan mode automatically.

What Should Happen?

After /clear, the conversation should reset to plan mode when defaultMode: "plan" is configured.

Error Messages/Logs

Steps to Reproduce

1. Create/edit ~/.claude/settings.json with:

```json
{
"permissions": {
"defaultMode": "plan"
}
}

1. Start Claude Code
2. Use Shift+Tab to switch to "Accept Edits" mode
3. Run /clear to clear the conversation
4. Observe that plan mode is not active (remains in Accept Edits mode)

Claude Model

Not sure / Multiple models

Is this a regression?

I don't know

Last Working Version

_No response_

Claude Code Version

2.1.19

Platform

Anthropic API

Operating System

macOS

Terminal/Shell

Terminal.app (macOS)

Additional Information

The conversation retains the previous permission mode (Accept Edits) instead of resetting to the configured default.