[BUG] [VS Code] Plan mode indicator stays selected but subsequent messages run under "Edit automatically" permissions

### 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?

When Plan mode is selected in the VS Code extension's mode indicator, asking a question causes Claude to answer normally (as expected for Plan mode). However, the mode indicator continues to display "Plan" as selected, but the next prompt sent in the same session is actually processed under "Edit automatically" permissions rather than Plan mode - Claude proceeds to make edits without presenting a plan for approval first. This creates a mismatch between the displayed mode and actual behavior, with no indication to the user that the mode silently changed.

### What Should Happen?

The mode indicator should accurately reflect the active permission mode at all times. If Plan mode is selected, every subsequent prompt in that session should be processed under Plan mode until explicitly changed.

### Error Messages/Logs

```shell

```

### Steps to Reproduce

1. Open a session in the VS Code extension
2. Click the mode indicator and select "Plan"
3. Ask a question or give a task — Claude answers/plans normally, mode indicator still shows "Plan"
4. Send a follow-up prompt in the same session
5. Observe: Claude makes edits directly instead of producing a plan, even though the indicator still shows "Plan" selected

### Claude Model

Opus

### Is this a regression?

Yes, this worked in a previous version

### Last Working Version

_No response_

### Claude Code Version

Claude 2.110.0 (dfb2ba) 2026-09-15T05:50:55.000Z

### Platform

Other

### Operating System

Windows

### Terminal/Shell

VS Code integrated terminal

### Additional Information

_No response_

Reproduce this in the VS Code extension on Windows using the listed steps, then trace how the Plan selection and subsequent session prompts determine permission mode. Verify whether the first question changes the stored mode despite the indicator remaining selected. Done means Plan remains active for every follow-up prompt until the user explicitly changes it, with the indicator matching the effective permissions.

Written by the indexing model from the issue text.