Expose reasoning effort level in status line JSON input

Feature Request

Is your feature request related to a problem?

The status line command receives JSON via stdin with model info, context window stats, cost, etc. However, the current reasoning effort level (e.g., low/medium/high or the numeric value like 85) is not included in the JSON payload.

This makes it impossible to display the active effort level in a custom status line, which would be useful for awareness of how Claude is currently configured — especially when toggling between effort levels during a session.

Describe the solution you'd like

Add a field to the status line JSON input, e.g.:

{
  "model": {
    "id": "claude-opus-4-6",
    "display_name": "Opus 4.6",
    "reasoning_effort": "medium"
  }
}

Or as a top-level field:

{
  "reasoning_effort": "medium"
}

Describe alternatives you've considered

• Tried reading from ~/.claude/.claude.json — effort level is not persisted there.
• Dumped the full status line JSON — confirmed the field is absent.
• No environment variable or config file exposes this at runtime.

Additional context

The effort level is a session-level setting that affects behavior significantly. Surfacing it in the status line would help users stay aware of their current configuration alongside model name, context usage, and cost.