Remote Control: add permission mode cycling from mobile app

Feature Request

When using Claude Code via Remote Control (/rc) from the Claude iOS/web app, there is no way to change the permission mode mid-session. On the CLI terminal, users can press Shift+Tab to cycle through permission modes (Default → Accept Edits → Plan → Default), but the mobile Remote Control interface has no equivalent control.

Problem

This creates a workflow gap for users who primarily interact via mobile Remote Control:

• Cannot grant edit permissions: If you start in a restrictive mode, you're stuck — every tool call gets denied with no way to approve
• Cannot enter Plan mode: Useful for switching to read-only analysis mid-session
• Cannot toggle Accept Edits: The most practical mode for hands-off mobile usage
• /permissions command is not recognized from the mobile interface either

Current Workaround

The user must physically go to the machine running the CLI session and press Shift+Tab on the terminal. This defeats the purpose of Remote Control.

Proposed Solution

Add a UI element in the mobile Remote Control interface that allows cycling or selecting permission modes, equivalent to Shift+Tab in the terminal. This could be:

1. A mode selector/dropdown in the mobile chat UI
2. A special /mode command recognized from Remote Control
3. A button/toggle in the session controls area

Related Issues

• #29214 — Mobile app shows permission prompts despite --dangerously-skip-permissions (permission mode inheritance is broken)
• #29006 — Enable Remote Control for Claude Desktop App

Environment

• Claude Code CLI on macOS
• Claude iOS app (Remote Control)
• Affects all permission modes when accessed via Remote Control