fix(background_review): inherit parent's reasoning_config to preserve Anthropic cache namespace

PR #17276 painstakingly pinned `_cached_system_prompt`, `session_start`,
`session_id`, and the toolset config on the background-review fork so its
outbound request body would byte-match the parent's and hit Anthropic's
exact-prefix cache. The contributor measured a ~26% end-to-end cost
reduction on Sonnet 4.5.

That optimization is currently being silently undone by a missing
`reasoning_config` kwarg. The fork's `AIAgent(...)` call omits it, so the
fork's `reasoning_config` defaults to `None`. `anthropic_adapter.build_anthropic_kwargs`
(line ~2165) then short-circuits the `thinking` / `output_config` block,
and the fork's request body lands in a DIFFERENT Anthropic cache namespace
from the parent's.

Result on the wire: 0 `cache_read_input_tokens`, full `cache_creation_input_tokens`
of the entire parent prefix — every single background review.

7 days of midagent.db traffic from one host running stock Hermes against
Anthropic Sonnet:

```
Background-review FIRST calls (the moment a review fork is born):
  count = 68
  cache_write tokens = 7,004,297
  cache_read tokens  = 1,016,335

Cost on Sonnet ($3.75/M write vs $0.30/M read):
  Spent on these writes:                      $26.27
  Cost if they had hit parent cache instead:   $2.10
  WASTED:                                     $24.16 / week / user
```

That is from one user. Multiply by Hermes's installed base for the full
impact.

Tested against api.anthropic.com directly (see refs/api-tests/ in the
attached investigation repo if needed):

| pair                                        | cache_r | cache_w |
|---------------------------------------------|---------|---------|
| parent fresh                                |       0 |  24,047 |
| parent same again                           |  24,047 |       0 |
| fork: appends 2 new tail msgs, thinking ON  |  24,047 |      22 |
| fork: appends 2 new tail msgs, thinking OFF |       0 |  24,047 |

Same fork-shape request, only difference is `thinking`. With the fix,
the fork hits the parent's full prefix and only writes the delta
(the `Review the conversation above…` prompt block, ~3-5K tokens).

One line in `agent/background_review.py`: pass
`reasoning_config=getattr(agent, "reasoning_config", None)` to the
`AIAgent(...)` constructor of the review fork. A short comment block
above it explains why so the next person who reads this code doesn't
re-introduce the regression.

`tests/run_agent/test_background_review_cache_parity.py` already covers
the system-prompt / session-id / toolset-config parity contracts that
PR #17276 introduced. I added:

* a `reasoning_config` attribute to `_make_agent_stub` so the stub has
  a non-None parent value the test can verify is propagated.
* `test_review_fork_inherits_parent_reasoning_config()` — asserts the
  fork's `AIAgent(...)` kwargs carry the parent's `reasoning_config`.
  Pre-fix this test fails with `None vs expected {'enabled': True, 'effort': 'medium'}`;
  post-fix all 4 tests in the file pass.

```
$ python -m pytest tests/run_agent/test_background_review_cache_parity.py -v
test_review_fork_inherits_parent_cached_system_prompt    PASSED
test_review_fork_pins_session_start_and_session_id       PASSED
test_review_fork_inherits_parent_toolset_config          PASSED
test_review_fork_inherits_parent_reasoning_config        PASSED  ← new
```

Also runs against the broader background-review test suite:
`test_background_review.py` (4), `test_background_review_summary.py` (8),
`test_background_review_toolset_restriction.py` (3) — 19/19 pass.

`agent/curator.py:1691` has the same omission for the umbrella-curation
fork, but curator's prompt is "curate all skills" — it shares no prefix
with any user conversation, so cache-parity is a non-issue there. Worth
auditing if the curator ever takes a parent conversation as input, but
not part of this PR.

The `agent/auxiliary_client.py:1006` `reasoning_config=None` hardcode is
intentional (title/summary one-shots on short prompts — per-call cost
of namespace flip is negligible) and is also out of scope.

agent/background_review.py

@@ -696,6 +696,10 @@ def _run_review_in_thread(
             if isinstance(_rt.get("command"), str) and _rt["command"]:
                 _fork_kwargs["acp_command"] = _rt["command"]
                 _fork_kwargs["acp_args"] = _rt.get("args") or []
+            # Match parent's reasoning config so the fork's ``thinking`` /
+            # ``output_config`` are byte-identical in the request body —
+            # Anthropic's cache key is namespaced by ``thinking`` presence.
+            _fork_kwargs["reasoning_config"] = getattr(agent, "reasoning_config", None)
             review_agent = AIAgent(
                 model=_rt.get("model") or agent.model,
                 max_iterations=16,

tests/run_agent/test_background_review_cache_parity.py

@@ -41,6 +41,9 @@ def _make_agent_stub(agent_cls):
     # Non-None so the test catches a missing-kwarg regression.
     agent.enabled_toolsets = ["memory", "skills", "terminal"]
     agent.disabled_toolsets = ["spotify", "feishu_doc"]
+    # Non-None so the test catches reasoning_config NOT being inherited —
+    # which would put the fork into a different Anthropic cache namespace.
+    agent.reasoning_config = {"enabled": True, "effort": "medium"}
     return agent
 
 
@@ -237,3 +240,49 @@ def test_review_fork_inherits_parent_toolset_config():
         f"disabled_toolsets mismatch: {captured.get('disabled_toolsets')!r} "
         f"vs expected {agent.disabled_toolsets!r}"
     )
+
+
+def test_review_fork_inherits_parent_reasoning_config():
+    """``reasoning_config`` parity: fork must inherit parent's value so the request body's ``thinking`` / ``output_config`` match (Anthropic cache is namespaced by ``thinking`` presence)."""
+    import run_agent
+
+    agent = _make_agent_stub(run_agent.AIAgent)
+
+    captured = {}
+
+    class _Recorder:
+        def __init__(self, *args, **kwargs):
+            captured["reasoning_config"] = kwargs.get("reasoning_config")
+            self._cached_system_prompt = None
+            self._memory_write_origin = None
+            self._memory_write_context = None
+            self._memory_store = None
+            self._memory_enabled = None
+            self._user_profile_enabled = None
+            self._memory_nudge_interval = None
+            self._skill_nudge_interval = None
+            self.suppress_status_output = None
+            self.session_start = None
+            self.session_id = None
+
+        def run_conversation(self, *args, **kwargs):
+            raise RuntimeError("stop after recording — don't actually call the API")
+
+        def shutdown_memory_provider(self):
+            pass
+
+        def close(self):
+            pass
+
+    with patch.object(run_agent, "AIAgent", _Recorder), \
+         patch("threading.Thread", _SyncThread):
+        agent._spawn_background_review(
+            messages_snapshot=[],
+            review_memory=True,
+            review_skills=False,
+        )
+
+    assert captured.get("reasoning_config") == agent.reasoning_config, (
+        f"reasoning_config mismatch: {captured.get('reasoning_config')!r} "
+        f"vs expected {agent.reasoning_config!r}"
+    )