refactor(tools): split wait_for_message into respond_to_user + wait_for_agents

One tool was doing three jobs (wait on the user, wait on other agents, and
- wrongly - wait for a long-running command), so the driver had to guess which
one an agent meant and used parent_id as the proxy: the root waits for a human,
everyone else waits for agents. That proxy is wrong, since the user can message
any agent from the TUI's agent tree.

Tool identity now carries the intent, and the coordinator records it as a
wait_kind that survives snapshot/restore:

  respond_to_user  -> wait_kind="user",   never auto-resumed (root or not)
  wait_for_agents  -> wait_kind="agents", auto-resumed on a 300s timer
  recovery exhaust -> wait_kind="stalled"

respond_to_user fuses the message and the yield into one call, so there is no
way to answer and then forget to stop - the two-step that gpt-4o-mini skipped
2/2 in live testing. Plain text still renders as before.

Auto-resume is also bounded now: an agent that re-parks after every timeout
burned a model turn every 300s for the rest of the scan (and, since parked
children notify their parent, spammed the parent's inbox on the same cycle).
After _MAX_IDLE_AUTO_RESUMES it stays parked until a real message arrives.

tests/test_e2e_budget_lifecycle.py

@@ -7,7 +7,7 @@ from unittest.mock import MagicMock, patch
 import pytest
 
 from strix.core import execution
-from strix.core.agents import AgentCoordinator
+from strix.core.agents import AgentCoordinator, WaitKind
 from strix.core.execution import _start_child_runner, run_agent_loop
 from strix.core.hooks import BudgetExceededError, ReportUsageHooks
 from strix.core.sessions import open_agent_session
@@ -42,23 +42,32 @@ class _FakeStream:
         hooks: ReportUsageHooks,
         context: dict[str, Any],
         agent: Any,
+        coordinator: AgentCoordinator,
     ) -> None:
         self._ledger = ledger
         self._hooks = hooks
         self._context = context
         self._agent = agent
+        self._coordinator = coordinator
         self.run_loop_exception: BaseException | None = None
         self.final_output = None
 
     async def stream_events(self) -> AsyncIterator[Any]:
+        agent_id = str(self._context.get("agent_id"))
         self._ledger.cost += COST_PER_CALL
-        self._ledger.calls.append(str(self._context.get("agent_id")))
+        self._ledger.calls.append(agent_id)
         ctx_wrapper = MagicMock()
         ctx_wrapper.context = self._context
         try:
             await self._hooks.on_llm_end(ctx_wrapper, self._agent, MagicMock())
         except Exception as exc:  # noqa: BLE001
             self.run_loop_exception = exc
+        # Stand in for the explicit yield tool a real turn ends with. Without it
+        # every turn looks like a forgotten tool call and burns the recovery
+        # budget, which is a different scenario from the one under test here.
+        if self._coordinator.statuses.get(agent_id) == "running":
+            wait_kind: WaitKind = "user" if self._context.get("parent_id") is None else "agents"
+            await self._coordinator.park_waiting(agent_id, wait_kind=wait_kind)
         items: tuple[Any, ...] = ()
         for item in items:
             yield item
@@ -67,7 +76,7 @@ class _FakeStream:
         return
 
 
-def _fake_runner(ledger: _FakeLedger) -> Any:
+def _fake_runner(ledger: _FakeLedger, coordinator: AgentCoordinator) -> Any:
     class _FakeRunner:
         @staticmethod
         def run_streamed(
@@ -80,7 +89,13 @@ def _fake_runner(ledger: _FakeLedger) -> Any:
             session: Any,  # noqa: ARG004
             hooks: ReportUsageHooks,
         ) -> _FakeStream:
-            return _FakeStream(ledger=ledger, hooks=hooks, context=context, agent=agent)
+            return _FakeStream(
+                ledger=ledger,
+                hooks=hooks,
+                context=context,
+                agent=agent,
+                coordinator=coordinator,
+            )
 
     return _FakeRunner
 
@@ -103,10 +118,10 @@ async def test_full_budget_lifecycle_reserve_then_cap(  # noqa: PLR0915
 ) -> None:
     ledger = _FakeLedger()
     hooks = ReportUsageHooks(model="test-model", max_budget_usd=MAX_BUDGET)
-    monkeypatch.setattr(execution, "Runner", _fake_runner(ledger))
+    coordinator = AgentCoordinator()
+    monkeypatch.setattr(execution, "Runner", _fake_runner(ledger, coordinator))
     monkeypatch.setattr(execution, "_compact_session", _noop_compact)
 
-    coordinator = AgentCoordinator()
     db_path = tmp_path / "agents.sqlite"
     sessions: list[Any] = []
     run_config = MagicMock()
@@ -218,7 +233,6 @@ async def test_respawned_children_after_reserve_never_spend(
     ledger = _FakeLedger()
     ledger.cost = 9.5
     hooks = ReportUsageHooks(model="test-model", max_budget_usd=MAX_BUDGET)
-    monkeypatch.setattr(execution, "Runner", _fake_runner(ledger))
     monkeypatch.setattr(execution, "_compact_session", _noop_compact)
 
     coordinator = AgentCoordinator()
@@ -230,6 +244,7 @@ async def test_respawned_children_after_reserve_never_spend(
     restored = AgentCoordinator()
     await restored.restore(snap)
     assert restored.reserve_stopped is True
+    monkeypatch.setattr(execution, "Runner", _fake_runner(ledger, restored))
 
     sessions: list[Any] = []
     with patch("strix.core.hooks.get_global_report_state", return_value=ledger):
@@ -264,7 +279,6 @@ async def test_resumed_parked_root_after_reserve_is_renotified_and_finalizes(
     ledger = _FakeLedger()
     ledger.cost = 9.0
     hooks = ReportUsageHooks(model="test-model", max_budget_usd=MAX_BUDGET)
-    monkeypatch.setattr(execution, "Runner", _fake_runner(ledger))
     monkeypatch.setattr(execution, "_compact_session", _noop_compact)
 
     coordinator = AgentCoordinator()
@@ -276,6 +290,7 @@ async def test_resumed_parked_root_after_reserve_is_renotified_and_finalizes(
     restored = AgentCoordinator()
     await restored.restore(snap)
     assert restored.reserve_stopped is True
+    monkeypatch.setattr(execution, "Runner", _fake_runner(ledger, restored))
 
     root_session = open_agent_session("root", tmp_path / "agents.sqlite")
     with patch("strix.core.hooks.get_global_report_state", return_value=ledger):
@@ -312,10 +327,10 @@ async def test_interactive_budget_pause_then_user_message_extends_and_resumes(
     ledger = _FakeLedger()
     ledger.cost = 9.0
     hooks = ReportUsageHooks(model="test-model", max_budget_usd=MAX_BUDGET, interactive=True)
-    monkeypatch.setattr(execution, "Runner", _fake_runner(ledger))
+    coordinator = AgentCoordinator()
+    monkeypatch.setattr(execution, "Runner", _fake_runner(ledger, coordinator))
     monkeypatch.setattr(execution, "_compact_session", _noop_compact)
 
-    coordinator = AgentCoordinator()
     coordinator.set_budget_extender(hooks.extend_budget)
     await coordinator.register("root", "strix", parent_id=None)
     root_session = open_agent_session("root", tmp_path / "agents.sqlite")