Slash commands not supported in /remote-control UI

When using /remote-control to continue a local Claude Code session from claude.ai/code or a mobile device, slash commands (e.g., /clear, /compact, /context, /rewind) typed in the remote UI are not processed as commands — they're sent as regular chat messages.

Steps to Reproduce

1. Start a Claude Code session locally
2. Run /remote-control to get a remote session link
3. Open the session in claude.ai/code or mobile
4. Type /clear (or any slash command) in the remote UI
5. Observe it's treated as plain text, not executed as a command

Expected Behavior

Slash commands from the remote UI should be recognized and executed by the local CLI process, the same way they work in the local terminal.

Current Behavior

Slash commands are only processed when typed in the local terminal. The remote UI has no way to trigger them.

Impact

Users working from the remote interface have no way to manage their session (clear context, compact, rewind, etc.) without switching back to the local terminal.

Suggestion

Intercept messages starting with / in the remote-control protocol and route them through the local CLI's command handler.