[Bug] `/clear` command desynchronizes mobile app state with terminal session

Bug Description

When using Claude Code remote control from the mobile app, sending a /clear command clears the session in the terminal as expected, but the mobile app UI does not reflect this change.

Steps to reproduce:

1. Start a remote control session.
2. Use the session from the mobile app (send a few prompts).
3. Send the /clear command.

Expected behavior:

• The terminal session is cleared.
• The mobile app state (conversation history and status) is also reset to match.

Actual behavior:

• The terminal session is cleared correctly.
• The mobile app conversation history remains uncleared.
• The session status stays "In Progress," preventing new prompts from being sent.
• Manually cancelling the request unblocks input, but the conversation history in the mobile app still appears uncleared.

Impact:
Workflow is blocked after every /clear command until the user manually cancels the pending request, and the mobile app never reflects the cleared state.

Environment Info

• Platform: darwin
• Terminal: ghostty
• Version: 2.1.85
• Feedback ID: d0a6777e-b02f-48c4-90cf-d967ae628e6f