[BUG] VS Code extension sessions don't show up in the Desktop app

### 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?

What's happening

I have a Claude Code session running in VS Code. It never appears in the Desktop app's session list, even though both are open on the same machine, same account, machine awake and online. At one point the Desktop app showed "Can't reach your computer — it may be asleep or offline," which was wrong — the machine was actively running the session the whole time.

Why

The VS Code extension and the Desktop app each launch their own separate claude process. I confirmed this with ps aux: two completely independent processes, one started by VS Code, one started by the Desktop app. The Desktop app only knows about sessions it itself launched — it has no way to see a session another app (like VS Code) started, even on the same machine.

The actual bug

The "Can't reach your computer" message is misleading. It implies the Desktop app once knew about this session and lost the connection. In reality it never knew about the session at all, so the message should either not appear, or say something more accurate.

Suggested fix

Either:

Make the Desktop app aware of sessions started by other Claude Code integrations on the same machine (VS Code, terminal), so everything shows up in one place, or
If that's not planned, fix the misleading "reconnecting" message for sessions the Desktop app was never tracking.
Environment

macOS, Desktop app v2.110.0, VS Code extension v2.1.270

### What Should Happen?

Either the Desktop app shows sessions started by other Claude Code integrations on the same machine (like VS Code), so all my sessions are visible in one place — or, if that's not supported, the "Can't reach your computer" message shouldn't appear for a session the Desktop app never launched and never tracked. Right now it shows a "reconnecting" message that implies a fixable connectivity problem, when actually the Desktop app just has no visibility into that session at all.

### Error Messages/Logs

```shell
# Session running in VS Code extension:
/Users//.vscode/extensions/anthropic.claude-code-2.1.270-darwin-arm64/resources/native-binary/claude \
--resume=387c8ce2-ef4e-40be-9787-170334d2acc0 --permission-mode auto ...

# Desktop app's own, separate session:
/Users//Library/Application Support/Claude/claude-code/2.1.271/claude.app/Contents/MacOS/claude \
--allowedTools mcp__ccd_session_mgmt__list_sessions,mcp__ccd_session_mgmt__get_session,... \
--permission-mode auto ...
```

### Steps to Reproduce

Open a project in VS Code with the Claude Code extension installed and start a session.
Separately open the Claude Code Desktop app, signed into the same account, on the same machine.
Check the Desktop app's session sidebar — the VS Code session never appears there.
Keep the VS Code session running for a while (machine stays awake and online the whole time).
At some point the Desktop app shows "Can't reach your computer — it may be asleep or offline. This session will reconnect when it's back," even though nothing is actually offline.

### Claude Model

Sonnet (default)

### Is this a regression?

Yes, this worked in a previous version

### Last Working Version

Last working version: N/A — this isn't a regression. I have no evidence VS Code extension sessions ever appeared in the Desktop app's session list; this appears to be how the two integrations have always worked (each tracking only its own sessions), not something that broke from a previously-working state.

### Claude Code Version

$ claude --version 2.1.183 (Claude Code)

### Platform

Anthropic API

### Operating System

macOS

### Terminal/Shell

Terminal.app (macOS)

### Additional Information

_No response_

Reproduce the issue by starting sessions from the VS Code extension and Desktop app, using the two Claude executable paths shown in the report as entry points. Trace how the Desktop app discovers and tracks sessions, then determine whether cross-integration visibility or a narrower message change is intended. Done means sessions are represented accurately and the Desktop app no longer shows a misleading offline or reconnecting message for an untracked session.

Written by the indexing model from the issue text.