feat(grok): reap abandoned interactive chats (M3)

An interactive intake/secretary chat the human abandoned (closed the tab without
confirming or stopping) leaked its container until the orchestrator restarted —
the wedged-grok reaper is task-driven and these run task_id=None, and an SSE
disconnect intentionally does NOT reap (so a page reload can reconnect).

Reap by IDLE TIME, not connection state: PrompterLiveRegistry tracks
last_activity (bumped on every push/deliver = a turn), and the 60s sweeper
retires sessions idle past ROBOCO_INTERACTIVE_IDLE_REAP_SECONDS (default 1800;
0 disables) via reap_intake_session / reap_secretary_session. An active or
page-reloaded chat that keeps exchanging turns stays fresh and is never reaped;
board-review-parked sessions (task_id set) are exempt. Provider-agnostic — fixes
the leak for both Claude and Grok interactive.

Tests: idle-only reap (active/parked/closed excluded), activity bump keeps a
session alive, threshold 0 disables. Gate green (ruff/mypy/xenon + prompter_live).

tests/unit/services/test_prompter_live.py

@@ -4,6 +4,7 @@ from __future__ import annotations
 
 import asyncio
 import json
+import time
 
 import httpx
 import pytest
@@ -22,6 +23,35 @@ def test_open_get_close() -> None:
     assert reg.get("s1") is None
 
 
+def test_idle_session_ids_reaps_only_abandoned_chats() -> None:
+    reg = PrompterLiveRegistry()
+    old = reg.open("idle", "intake-1")
+    old.last_activity = time.monotonic() - 4000  # silent for >1h
+    reg.open("fresh", "intake-1")  # just opened — active
+    parked = reg.open("parked", "intake-1")  # board-review parked
+    parked.last_activity = time.monotonic() - 4000
+    parked.task_id = "task-9"
+    reg.open("done", "secretary-1")
+    reg.close("done")  # closed sessions excluded
+
+    idle = dict(reg.idle_session_ids(1800))
+    assert "idle" in idle and idle["idle"] == "intake-1"  # abandoned -> reaped
+    assert "fresh" not in idle  # active -> kept
+    assert "parked" not in idle  # board-review parked -> exempt
+    assert "done" not in idle  # closed -> excluded
+    # Disabled when threshold <= 0.
+    assert reg.idle_session_ids(0) == []
+
+
+def test_activity_bump_keeps_session_alive() -> None:
+    reg = PrompterLiveRegistry()
+    s = reg.open("s1", "intake-1")
+    s.last_activity = time.monotonic() - 4000
+    assert ("s1", "intake-1") in reg.idle_session_ids(1800)
+    reg.push("s1", {"kind": "text", "text": "hi"})  # an agent turn = activity
+    assert reg.idle_session_ids(1800) == []  # no longer idle
+
+
 def test_close_by_agent_closes_matching_sessions_with_error() -> None:
     reg = PrompterLiveRegistry()
     reg.open("s1", "intake-1")