[BUG] Remote Control: sending from mobile silently fails (message disappears), reading works fine

### Preflight Checklist

- [x] I have searched [existing issues](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20state%3Aopen%20label%3Abug) and this hasn't been reported yet
- [x] This is a single bug report (please file separate reports for different bugs)
- [x] I am using the latest version of Claude Code

### What's Wrong?

When using `claude remote-control`, messages typed and sent from the phone (mobile web session) never reach the CLI. Desktop -> phone works fine (I can read Claude's replies live on the phone), but anything typed and sent from the phone just disappears: no error shown, no queued/pending state, nothing arrives on the desktop side.

Cleared app data on the phone and started a brand new remote-control session, got the exact same failure both times.

Also tested on two completely different networks (restaurant wifi and mobile carrier 5G data) with identical results, which rules out a local firewall/network issue like the one identified as the root cause in #62284 (antivirus blocking traffic).

### What Should Happen?

Messages sent from the phone during a Remote Control session should reach the CLI and appear in the conversation, the same way messages typed on the desktop reach the phone.

### Error Messages/Logs

```shell

```

### Steps to Reproduce

1. On desktop, run `claude remote-control` inside a project folder.
2. Scan the QR code with the phone to connect.
3. From the desktop, type a message; confirm it shows up and gets a reply visible on the phone (read direction works).
4. From the phone, type any message and send it.
5. Message disappears from the phone's input with no error, and never appears on the desktop CLI session.

Reproduced on a brand new remote-control session after clearing the phone app's data, and on two different networks (restaurant wifi, mobile 5G).

### Claude Model

None

### Is this a regression?

Yes, this worked in a previous version

### Last Working Version

_No response_

### Claude Code Version

2.1.236 (Claude Code)

### Platform

Anthropic API

### Operating System

Windows

### Terminal/Shell

Windows Terminal

### Additional Information

Related reports with similar symptoms but a different confirmed root cause (local network/antivirus), which I've ruled out by testing on two unrelated networks: #62284, #34619, #45946.

Native Windows install (claude.exe at %USERPROFILE%\.local\bin), not the npm package.

Start by reproducing the failure with `claude remote-control` in Windows Terminal, following the listed desktop-to-phone and phone-to-desktop steps, then trace the remote-control message path; the issue names no source file or test. Done means a phone-sent message reliably appears in the desktop CLI conversation without disappearing, while desktop-to-phone behavior remains intact.

由索引模型根据 Issue 内容生成。