feat(cli): track background subagents in the status bar (#51441)

The classic prompt_toolkit status bar already shows two background
indicators: ▶ N (/background agent threads) and ⚙ N (shell processes
spawned by terminal(background=true)). Background/async subagents
(delegate_task batches and background single delegations) had no
indicator despite being long-running work the user should be able to
see at a glance.

Add a third indicator ⛓ N sourced from
tools.async_delegation.active_count() — the count of delegations still
in the 'running' state. Renders in the plain-text builder and the
styled-fragment builder across the same width tiers as the other two
(omitted on the narrow <52 tier), guarded so a raising active_count()
leaves the snapshot at 0.

tests/cli/test_cli_background_status_indicator.py

@@ -189,3 +189,82 @@ def test_indicators_independent_agents_and_processes(monkeypatch):
     rendered = "".join(text for _style, text in frags)
     assert "▶ 1" in rendered
     assert "⚙ 2" in rendered
+
+
+# ── Background/async subagent indicator (⛓ N) ─────────────────────────────
+# Source of truth is tools.async_delegation.active_count() — the count of
+# delegate_task delegations (batch + background single) still in the
+# "running" state. Distinct from ▶ (/background agent threads) and ⚙ (shell
+# processes); all three can be active at once.
+
+
+def _patch_async_active(monkeypatch, count: int) -> None:
+    import tools.async_delegation as ad_mod
+    monkeypatch.setattr(ad_mod, "active_count", lambda: count)
+
+
+def test_snapshot_reports_zero_when_no_background_subagents(monkeypatch):
+    cli_obj = _make_cli()
+    _patch_async_active(monkeypatch, 0)
+    snap = cli_obj._get_status_bar_snapshot()
+    assert snap["active_background_subagents"] == 0
+
+
+def test_snapshot_counts_live_background_subagents(monkeypatch):
+    cli_obj = _make_cli()
+    _patch_async_active(monkeypatch, 4)
+    snap = cli_obj._get_status_bar_snapshot()
+    assert snap["active_background_subagents"] == 4
+
+
+def test_snapshot_safe_when_async_active_count_raises(monkeypatch):
+    """If active_count() raises the snapshot stays at 0; no propagate."""
+    cli_obj = _make_cli()
+    import tools.async_delegation as ad_mod
+
+    def _boom():
+        raise RuntimeError("boom")
+
+    monkeypatch.setattr(ad_mod, "active_count", _boom)
+    snap = cli_obj._get_status_bar_snapshot()
+    assert snap["active_background_subagents"] == 0
+
+
+def test_plain_text_status_shows_subagent_indicator_when_active(monkeypatch):
+    cli_obj = _make_cli()
+    _patch_async_active(monkeypatch, 3)
+    text = cli_obj._build_status_bar_text(width=80)
+    assert "⛓ 3" in text
+
+
+def test_plain_text_status_omits_subagent_indicator_when_idle(monkeypatch):
+    cli_obj = _make_cli()
+    _patch_async_active(monkeypatch, 0)
+    text = cli_obj._build_status_bar_text(width=80)
+    assert "⛓" not in text
+
+
+def test_fragments_include_subagent_segment_when_active(monkeypatch):
+    cli_obj = _make_cli()
+    _patch_async_active(monkeypatch, 2)
+    cli_obj._status_bar_visible = True
+    cli_obj._get_tui_terminal_width = lambda: 120  # type: ignore[method-assign]
+    frags = cli_obj._get_status_bar_fragments()
+    rendered = "".join(text for _style, text in frags)
+    assert "⛓ 2" in rendered
+
+
+def test_all_three_background_indicators_independent(monkeypatch):
+    """▶ (agent tasks), ⚙ (shell processes), ⛓ (subagents) all coexist."""
+    cli_obj = _make_cli()
+    cli_obj._background_tasks = {"bg_a": _stub_thread()}
+    _patch_process_registry(monkeypatch, 2)
+    _patch_async_active(monkeypatch, 5)
+    cli_obj._status_bar_visible = True
+    cli_obj._get_tui_terminal_width = lambda: 120  # type: ignore[method-assign]
+    frags = cli_obj._get_status_bar_fragments()
+    rendered = "".join(text for _style, text in frags)
+    assert "▶ 1" in rendered
+    assert "⚙ 2" in rendered
+    assert "⛓ 5" in rendered
+