Background tasks (run_in_background) are invisible: no statusline payload field, no UI badge — and sessions with live tasks resist deletion with no explanation

Environment

• Claude Code 2.1.215, macOS (Darwin 25.5), terminal + agents view
• Session type: background session (claude --bg) in a git worktree

What happened

A long autonomous run used several run_in_background Bash tasks (CI deploy watchers, up to ~30 min each). While any of them were running:

1. Nothing anywhere in the UI indicated they existed — not the custom statusline, not the built-in footer badges (the ← N agent badge counts subagents/agent-teams, not background bash tasks), not the agents view.
2. Deleting the session from the agents view (Ctrl+X) silently failed / the session kept reappearing as each finishing task re-invoked it. From the user's perspective the chat 'refused to die' with no explanation, repeatedly, until the last watcher happened to finish — at which point teardown succeeded instantly.

The protection itself (don't tear down a session with live background work) seems right; the invisibility makes it indistinguishable from a bug.

Why a custom statusline can't fix this

Per the statusline docs' full JSON schema, the stdin payload carries model, workspace, cost, context_window, rate_limits, session_id/session_name, pr, worktree, effort, etc. — no field describing running background tasks, their count, or active subagents. So user-side scripts have nothing to render.

Requested

Any/all of, in rough priority order:

1. Agents-view deletion refusal explains itself: 'N background tasks still running — stop the session first' (this alone would have eliminated the confusion).
2. background_task_count (or a small tasks array: id, description, started_at) in the statusline JSON payload, so custom statuslines can render e.g. ⏳ 2 bg.
3. A built-in footer badge for running background tasks, symmetric with the existing agent badge.

Repro sketch

1. In any session: Bash(run_in_background: true) with a long sleep-loop.
2. Observe statusline + footer: no indicator.
3. From claude agents, try Ctrl+X on that session while the task runs → deletion doesn't take, no reason shown.