[BUG] Remote Control: mobile client stuck on 'sending' after /clear command

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] I can reproduce the bug with the latest version of Claude Code

Bug Description

When using Remote Control from a mobile device (claude.ai/code), sending the /clear slash command causes two problems:

1. Previous conversation is NOT cleared on mobile — all old messages remain visible on screen
2. Mobile client gets stuck on "sending" — no further interaction is possible

Meanwhile, the CLI side clears the conversation successfully. The mobile client is completely out of sync.

Steps to Reproduce

1. Start a Claude Code CLI session with /remote-control enabled
2. Connect to the session from a mobile browser (claude.ai/code)
3. Have some conversation history in the session
4. From the mobile client, type /clear and send
5. Observe: CLI terminal clears the conversation successfully
6. Observe: Mobile client still shows all previous messages — conversation is not cleared
7. Observe: Mobile client is stuck showing "sending..." — never resolves, no further input possible

Expected Behavior

After /clear is sent from the mobile client:

• The CLI session clears (this works correctly)
• The mobile client should clear all previous conversation messages from the UI
• The mobile client should return to an interactive state, ready for new input

Actual Behavior

• The CLI session clears correctly
• The mobile client does NOT clear the previous conversation — old messages remain on screen
• The mobile client gets stuck on "sending" and becomes unresponsive
• Requires a page refresh / reconnect to recover

Root Cause Hypothesis

Slash commands like /clear that reset the entire session state are not propagating a proper state-sync event back to the Remote Control client. The mobile client is waiting for a response to its message, but the session reset likely destroys the pending response context, leaving the client with stale conversation history and a hung request.

Environment

• Platform: Windows 11
• Claude Code version: Latest (bypass mode)
• Remote Control client: Mobile browser (claude.ai/code)