Remote control: responses not visible on phone, only in laptop terminal

Bug Description

When using the remote control feature, the phone client can successfully send prompts, but responses only appear in the laptop terminal — not on the phone's remote control interface. The phone UI either spins indefinitely or freezes after sending a prompt.

Steps to Reproduce

1. Start claude remote-control on laptop (inside tmux)
2. Scan QR code / open URL on phone
3. Send a prompt from the phone — it reaches the laptop and Claude responds
4. Response appears in the laptop terminal but does not render on the phone
5. Phone UI shows a spinner or freezes
6. Can still send a second prompt from phone (it also reaches the laptop), but response again only shows in terminal

Expected Behavior

Responses should appear on the phone's remote control interface, not just in the laptop terminal.

Environment

• Claude Code CLI on WSL2 (Linux 5.15.153.1-microsoft-standard-WSL2)
• Phone: Claude mobile app (iOS)
• Session started locally on laptop, connected via remote control from phone