feat(R04): run every Cowork turn through ConversationApplicationService

R04-T03 — the turn lifecycle, extracted from `core/chat_agent.py::run_cowork`
into `application/conversations/`. The 260-line body mixed the lifecycle (step
budget, cancel checks, guard -> preview -> gate -> execute ordering, sandbox
tidy-up) with the machinery doing each step, and reaching any of it meant
standing up a Qt widget and a worker thread. It is now a plain object driven
through two Protocols and six callables (`turn_runtime.py`), with the concrete
`core/*` wiring confined to `core_runtime_adapter.py` — the same shape R03 used
for routing. Faithful port, not an improvement pass: where the original had a
quirk (the step-ceiling note only merges into the answer when the last message
is the assistant's) the quirk is preserved and commented.

R04-T04 — `ui/cowork_tab.py::build_job` no longer calls run_cowork. It captures
the widget's state at submit time, builds the request via the new
`cowork_turn_request.py` and executes it. `execute(..., messages=...)` hands the
widget's own list over because `_reattach_running_turn` replays from it WHILE
the worker appends and `_finalize_turn` slices it afterwards — a private list
would break both silently.

R04-T05 — `core/task_executors.py`'s cowork branch shares the same engine. All
five unattended-run behaviours stay put (plan reminder, history_ready, History
autosave per assistant message, timeout notice, plan_incomplete_reason), and
`_unattended_prompt` now expresses the load-bearing prefix order in one
readable call instead of three successive rebindings.

Verification: 74 new tests (364 passed, 1 skipped overall; check_imports PASS).
The two that matter most:
- `test_conversation_service_parity.py` runs the same scripted turn through
  run_cowork AND the service and compares the event stream, the resulting
  conversation and the advertised tool list across 7 scenarios;
- `test_task_executor_turn.py` was written BEFORE the migration and passed 8/8
  against the old code, then unchanged against the new.

Known: `ui/cowork_tab.py` (416 -> 455) and `core/task_executors.py` (476 -> 524)
stay above the 400-LOC limit. Both were already over it before this change;
bringing them under needs the R08 / R07 decompositions.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

tests/integration/test_task_executor_turn.py

@@ -0,0 +1,191 @@
+"""R04-T05 — the Schedule Task runner's cowork branch, pinned before and after.
+
+Written against the CURRENT ``_run_agent`` first, as the safety net for moving it
+onto ``ConversationApplicationService``: an unattended run has five behaviours the
+interactive path does not have (the plan reminder prefixed to the prompt, the
+session registered in History before the model starts, a re-save after every
+assistant message, the timeout notice, and the "did the agent's own checklist
+finish?" report), and none of them was covered by a test.
+
+Everything is isolated from the user's real config: history goes to ``tmp_path``
+via ``history.custom_dir`` and the AI guardrails are off, so no run touches
+``~/.cowork_local`` or calls a model to review a prompt.
+"""
+
+from __future__ import annotations
+
+import copy
+import json
+from pathlib import Path
+from typing import Any, Dict, List, Optional
+
+from cowork_local.config import DEFAULT_CONFIG, AppConfig
+from cowork_local.core import task_executors
+from cowork_local.tests.fakes.fake_provider import FakeProvider
+
+
+class _FakeCtx:
+    """The ``AppContext`` surface ``_run_agent`` touches."""
+
+    def __init__(self, config: AppConfig, provider: FakeProvider) -> None:
+        self.config = config
+        self._provider = provider
+
+    def build_active_provider(self) -> FakeProvider:
+        return self._provider
+
+    def build_provider_for(self, name=None, model=None) -> FakeProvider:
+        return self._provider
+
+
+def _config(tmp_path: Path) -> AppConfig:
+    data = copy.deepcopy(DEFAULT_CONFIG)
+    # Keep the run entirely offline and off the real config dir.
+    data["agent_security"]["enabled"] = False
+    data["history"]["custom_dir"] = str(tmp_path / "history")
+    return AppConfig(data)
+
+
+def _run(tmp_path: Path, provider: FakeProvider, *, prompt: str = "write the report",
+         timeout_sec: Optional[int] = None, admin_agent: Any = None):
+    """Run one cowork task and return ``(result_tuple, events, config)``."""
+    out_dir = tmp_path / "run"
+    out_dir.mkdir(parents=True, exist_ok=True)
+    config = _config(tmp_path)
+    events: List[Dict[str, Any]] = []
+
+    result = task_executors._run_agent(
+        _FakeCtx(config, provider), "cowork", prompt, out_dir,
+        events.append, lambda: False, title="Weekly report",
+        timeout_sec=timeout_sec, admin_agent=admin_agent,
+    )
+    return result, events, config
+
+
+def _saved_conversation(config: AppConfig) -> Dict[str, Any]:
+    """The single conversation the run wrote into the isolated history folder."""
+    files = list(Path(config.history_dir()).rglob("*.json"))
+    assert len(files) == 1, f"expected one saved conversation, found {files}"
+    return json.loads(files[0].read_text(encoding="utf-8"))
+
+
+# --------------------------------------------------------------------------- #
+def test_a_cowork_task_returns_the_final_answer(tmp_path: Path) -> None:
+    provider = FakeProvider()
+    provider.queue_response(content="Report is ready.")
+
+    (answer, timed_out, incomplete), _events, _config = _run(tmp_path, provider)
+
+    assert answer == "Report is ready."
+    assert timed_out is False
+    assert incomplete == ""
+
+
+def test_the_plan_reminder_is_prefixed_to_the_prompt(tmp_path: Path) -> None:
+    # An unattended run has nobody watching, so the agent is pushed to keep its
+    # own checklist honest. The reminder must lead the message.
+    provider = FakeProvider()
+    provider.queue_response(content="ok")
+
+    _run(tmp_path, provider, prompt="write the report")
+
+    sent = provider.call_history[0][-1]["content"]
+    assert sent.startswith("This runs unattended (Schedule Task)")
+    assert sent.endswith("write the report")
+
+
+def test_an_admin_agent_persona_sits_between_the_reminder_and_the_prompt(
+        tmp_path: Path) -> None:
+    class _Agent:
+        # An admin agent may pin its own provider/model; blank means "use the
+        # machine's Settings default", which is what build_agent_provider reads.
+        provider = ""
+        model = ""
+
+        def effective_prompt(self) -> str:
+            return "You are the reporting agent."
+
+    provider = FakeProvider()
+    provider.queue_response(content="ok")
+
+    _run(tmp_path, provider, prompt="write the report", admin_agent=_Agent())
+
+    sent = provider.call_history[0][-1]["content"]
+    assert sent.index("This runs unattended") < sent.index("You are the reporting agent.")
+    assert sent.index("You are the reporting agent.") < sent.index("write the report")
+
+
+def test_the_session_is_announced_once_it_exists_on_disk(tmp_path: Path) -> None:
+    # The scheduler refreshes History on this event, so it must not fire before
+    # the conversation is really there.
+    provider = FakeProvider()
+    provider.queue_response(content="ok")
+
+    _result, events, config = _run(tmp_path, provider)
+
+    ready = [e for e in events if e["type"] == "history_ready"]
+    assert len(ready) == 1
+    assert ready[0]["session_id"]
+    assert _saved_conversation(config)["session_id"] == ready[0]["session_id"]
+
+
+def test_the_saved_conversation_carries_the_answer_and_the_task_title(
+        tmp_path: Path) -> None:
+    provider = FakeProvider()
+    provider.queue_response(content="Report is ready.")
+
+    _result, _events, config = _run(tmp_path, provider)
+
+    saved = _saved_conversation(config)
+    assert saved["title"] == "[Task] Weekly report"
+    assert saved["messages"][-1] == {"role": "assistant", "content": "Report is ready."}
+
+
+def test_an_unfinished_checklist_is_reported_back_to_the_scheduler(
+        tmp_path: Path) -> None:
+    # The agent ticked no step to done, so the task must not be called finished
+    # just because no exception was raised.
+    provider = FakeProvider()
+    provider.queue_response(
+        content="Working on it.",
+        tool_calls=[{"id": "c1", "name": "update_plan",
+                     "arguments": {"steps": [{"title": "Draft", "status": "running"}]}}],
+    )
+    provider.queue_response(content="Stopping here.")
+
+    (_answer, _timed_out, incomplete), _events, _config = _run(tmp_path, provider)
+
+    assert incomplete
+    assert "Draft" in incomplete
+
+
+def test_a_finished_checklist_reports_nothing_outstanding(tmp_path: Path) -> None:
+    provider = FakeProvider()
+    provider.queue_response(
+        content="Done.",
+        tool_calls=[{"id": "c1", "name": "update_plan",
+                     "arguments": {"steps": [{"title": "Draft", "status": "done"}]}}],
+    )
+    provider.queue_response(content="All done.")
+
+    (_answer, _timed_out, incomplete), _events, _config = _run(tmp_path, provider)
+
+    assert incomplete == ""
+
+
+def test_running_out_of_time_appends_the_timeout_notice_to_the_conversation(
+        tmp_path: Path) -> None:
+    # A negative timeout puts the deadline in the past, which is the only
+    # deterministic way to exercise a wall-clock branch in a unit test.
+    provider = FakeProvider()
+    provider.queue_response(content="never gets there")
+
+    (answer, timed_out, incomplete), events, config = _run(
+        tmp_path, provider, timeout_sec=-1)
+
+    assert timed_out is True
+    assert incomplete == ""          # a timeout is not an unfinished checklist
+    assert "quá thời gian chờ" in answer
+    assert any(e["type"] == "assistant_done" and "quá thời gian chờ" in e["content"]
+               for e in events)
+    assert "quá thời gian chờ" in _saved_conversation(config)["messages"][-1]["content"]