Desktop app Code tab mode picker missing "auto" and "bypass" modes

Summary

The desktop app's Code tab mode picker only exposes three permission modes (Ask permissions, Accept edits, Plan mode). The newer auto and bypass modes are not selectable from the UI, even though the underlying Claude Code engine supports them on the same account.

Environment

• Desktop app: Claude for Desktop 1.8555.0 (com.anthropic.claudefordesktop), macOS 15
• Claude Code CLI: 2.1.148
• Model: Opus 4.7 (1M context)
• Plan: Claude Team
• ~/.claude/settings.json has "defaultMode": "auto"

Repro

1. Open the desktop app, switch to the Code tab on a project.
2. Open the mode picker (⇧⌘M) — only three modes are listed.
3. In a regular terminal or in the desktop app's embedded terminal, run claude against the same project/account. Status line shows auto mode on (shift+tab to cycle).

Expected

Mode picker lists all permission modes the engine supports, matching the CLI (including auto and bypass).

Actual

Picker is capped at the legacy three modes. defaultMode: "auto" in settings.json is ignored by the desktop UI (the engine still honors it when invoked via the embedded terminal).

Screenshot below: left = desktop app picker, right = same account in CLI with auto mode active.

<img width="1258" height="402" alt="Image" src="https://github.com/user-attachments/assets/8feb85d0-f06e-42fd-9097-78c38aa0b75f" />