fix(gateway): make bg-process reset TTL configurable + surface session-scoped processes

Follow-up to the cherry-picked #29212 (#29177):

- Promote the 24h stale-process threshold to config.yaml
  (session_reset.bg_process_max_age_hours) instead of a hardcoded
  constant. 0 disables the cutoff (legacy: any live process blocks reset).
  Wired through GatewayConfig.default_reset_policy in gateway/run.py.
- Bug 2: process(action=list) now resolves the gateway session_key from
  the contextvar and surfaces session-scoped background processes (a
  forgotten preview server under a different task), flagged
  session_scoped — so the agent/user can discover and kill the blocker.
  Previously the task-scoped list returned [] and the blocker was invisible.
- Tests: config round-trip for the new field, cross-task list visibility.
- Docs: messaging session-reset section.

tests/gateway/test_config.py

@@ -138,26 +138,31 @@ class TestGetConnectedPlatforms:
 
 class TestSessionResetPolicy:
     def test_roundtrip(self):
-        policy = SessionResetPolicy(mode="idle", at_hour=6, idle_minutes=120)
+        policy = SessionResetPolicy(mode="idle", at_hour=6, idle_minutes=120,
+                                    bg_process_max_age_hours=48)
         d = policy.to_dict()
         restored = SessionResetPolicy.from_dict(d)
         assert restored.mode == "idle"
         assert restored.at_hour == 6
         assert restored.idle_minutes == 120
+        assert restored.bg_process_max_age_hours == 48
 
     def test_defaults(self):
         policy = SessionResetPolicy()
         assert policy.mode == "both"
         assert policy.at_hour == 4
         assert policy.idle_minutes == 1440
+        assert policy.bg_process_max_age_hours == 24
 
     def test_from_dict_treats_null_values_as_defaults(self):
         restored = SessionResetPolicy.from_dict(
-            {"mode": None, "at_hour": None, "idle_minutes": None}
+            {"mode": None, "at_hour": None, "idle_minutes": None,
+             "bg_process_max_age_hours": None}
         )
         assert restored.mode == "both"
         assert restored.at_hour == 4
         assert restored.idle_minutes == 1440
+        assert restored.bg_process_max_age_hours == 24
 
     def test_from_dict_coerces_quoted_false_notify(self):
         restored = SessionResetPolicy.from_dict({"notify": "false"})

tests/tools/test_process_registry.py

@@ -416,6 +416,34 @@ class TestListSessions:
         assert len(result) == 1
         assert result[0]["session_id"] == "proc_1"
 
+    def test_session_key_surfaces_cross_task_processes(self, registry):
+        """A bg process under the same gateway session but a DIFFERENT task is
+        surfaced when session_key is passed, and flagged session_scoped (#29177).
+        """
+        # Current turn's task = "t_now"; forgotten preview server = "t_old"
+        # but both share gateway session_key "gw1".
+        own = _make_session(sid="proc_own", task_id="t_now")
+        own.session_key = "gw1"
+        forgotten = _make_session(sid="proc_forgotten", task_id="t_old")
+        forgotten.session_key = "gw1"
+        other = _make_session(sid="proc_other", task_id="t_x")
+        other.session_key = "gw_other"
+        registry._running[own.id] = own
+        registry._running[forgotten.id] = forgotten
+        registry._running[other.id] = other
+
+        # Task-only (legacy) view sees just the current task's process.
+        legacy = registry.list_sessions(task_id="t_now")
+        assert {r["session_id"] for r in legacy} == {"proc_own"}
+
+        # With session_key, the forgotten process under the same gateway
+        # session is surfaced and flagged; the unrelated session is not.
+        result = registry.list_sessions(task_id="t_now", session_key="gw1")
+        by_id = {r["session_id"]: r for r in result}
+        assert set(by_id) == {"proc_own", "proc_forgotten"}
+        assert by_id["proc_forgotten"].get("session_scoped") is True
+        assert "session_scoped" not in by_id["proc_own"]
+
     def test_list_entry_fields(self, registry):
         s = _make_session(output="preview text")
         registry._running[s.id] = s