[Feature Request] Add running task information to status line JSON

Bug Description
Feature Request: Add running task information to status line JSON

Summary
Add task/agent tracking data to the JSON input passed to status line scripts, enabling users to display currently running background tasks, agents, and remote sessions in their status bar.

Requested additions to status line JSON:

{
"tasks": {
"count": 3,
"background_shells": 1,
"agents": 2,
"remote_sessions": 0,
"items": [
{ "id": "shell_abc123", "type": "shell", "description": "pnpm dev" },
{ "id": "agent_def456", "type": "agent", "subagent_type": "Explore" },
{ "id": "agent_ghi789", "type": "agent", "subagent_type": "code-reviewer" }
]
}
}

Use case

• Monitor agent spawning during complex tasks
• Know when background processes are still running
• Debug long-running operations
• Better visibility into Claude Code's parallel execution

Minimal version
Even just a task_count integer would be valuable:
{ "task_count": 3 }

Environment Info

• Platform: darwin
• Terminal: ghostty
• Version: 2.0.76
• Feedback ID: 51cf52ca-b684-4602-9c16-97c732dc03dc

Errors

[{"error":"Error: NON-FATAL: Lock acquisition failed for /Users/adam/.local/share/claude/versions/2.0.76 (expected in multi-process scenarios)\n    at XZR (/$bunfs/root/claude:2430:2165)\n    at fUA (/$bunfs/root/claude:2430:1885)\n    at processTicksAndRejections (native:7:39)","timestamp":"2026-01-05T21:04:28.272Z"}]