[BUG] VS Code extension ignores remoteControlAtStartup setting from ~/.claude.json

Preflight Checklist

• [x] I have searched existing issues to make sure this isn't a duplicate
• [x] This is a single bug report (not bundling multiple bugs)
• [x] I am using the latest version of Claude Code

What's wrong?

The VS Code extension does not auto-enable Remote Control on session start, even though remoteControlAtStartup is set to true in ~/.claude.json. The setting works correctly in the CLI terminal — Remote Control starts automatically. In VS Code, I have to manually run /remote-control each session.

What should happen?

When remoteControlAtStartup: true is set in ~/.claude.json, the VS Code extension should auto-enable Remote Control on session start, same as the CLI does.

Steps to reproduce

1. Run /config in Claude Code CLI and enable "Enable Remote Control for all sessions"
2. Verify ~/.claude.json contains "remoteControlAtStartup": true
3. Open a new Claude Code session in the CLI terminal — Remote Control starts automatically ✅
4. Open a new Claude Code session in the VS Code extension — Remote Control does NOT start automatically ❌
5. /remote-control works when run manually in VS Code, so the feature itself is supported

Is this a regression?

I don't know

Claude Code Version

2.1.87

Platform

Anthropic API

Operating System

macOS

Terminal/Shell

VS Code

Additional Information

Related issues: #29929 (CLI persistence bug, closed as dupe of #29266), #28951 (older issue about /rc not supported in VS Code — but /remote-control now works in VS Code, just not the auto-enable).