Expose Remote Control connection state to custom status line commands

Feature request

The status line stdin JSON has no field for Remote Control. A custom statusLine command cannot tell whether the session currently has an active Remote Control connection (started with /remote-control or /rc, or via remoteControlAtStartup).

Why this matters

• The built-in footer shows an "/rc active" indicator, but a custom statusLine hides most footer hints. Users who replace the status line lose the only visible sign that the session is reachable remotely.
• Remote Control lets someone drive the session from claude.ai/code, so knowing whether it is connected is useful at a glance.
• Current workarounds are weak:
• CLAUDE_CODE_BRIDGE_SESSION_ID is documented as set in Bash tool and hook subprocesses while a connection is active, but the docs do not say status line commands inherit it.
• remoteControlAtStartup only shows configured intent, not live state.
• No hook event fires on connect or disconnect, so a hook cannot maintain a marker file reliably.

Proposed change

Add a field to the status line JSON, for example:

"remote_control": {
  "connected": true,
  "session_id": "..."
}

with the object absent or connected: false when no connection is active. Alternatively, document that CLAUDE_CODE_BRIDGE_SESSION_ID is exported to the status line command's environment.

Environment

• Claude Code version: 2.1.300
• OS: Linux