feat(aux): translate extra_body.reasoning into Codex Responses API (#17004)

Auxiliary callers that configure reasoning via
auxiliary.<task>.extra_body.reasoning were having that config silently
dropped by the Codex Responses adapter — it only forwarded
messages/model/tools through to responses.stream(), never translating
chat.completions-shaped reasoning hints into the Responses API's
top-level reasoning + include fields.

Mirror the main-agent translation from agent/transports/codex.py:
- extra_body.reasoning.effort → resp_kwargs.reasoning.{effort, summary:"auto"}
- 'minimal' → 'low' clamp (Codex backend rejects 'minimal')
- Always include ['reasoning.encrypted_content'] when reasoning is enabled
- {'enabled': False} → omit reasoning and include entirely
- Non-dict reasoning values are ignored defensively

Reported by @OP (Apr 26 feedback bundle).

## Changes
- agent/auxiliary_client.py: _CodexCompletionsAdapter.create() now reads
  and translates extra_body.reasoning before calling responses.stream()
- tests/agent/test_auxiliary_client.py: 9 new tests covering all effort
  levels, the minimal→low clamp, the disabled path, the no-op paths,
  and defensive handling of wrong-shape inputs

Co-authored-by: teknium1 <teknium@users.noreply.github.com>

agent/auxiliary_client.py

@@ -410,6 +410,33 @@ class _CodexCompletionsAdapter:
         # Note: the Codex endpoint (chatgpt.com/backend-api/codex) does NOT
         # support max_output_tokens or temperature — omit to avoid 400 errors.
 
+        # Translate extra_body.reasoning (chat.completions shape) into the
+        # Responses API's top-level reasoning + include fields.  Mirrors
+        # agent/transports/codex.py::build_kwargs() so auxiliary callers
+        # that configure reasoning via auxiliary.<task>.extra_body get the
+        # same behavior as the main agent's Codex transport.
+        extra_body = kwargs.get("extra_body") or {}
+        if isinstance(extra_body, dict):
+            reasoning_cfg = extra_body.get("reasoning")
+            if isinstance(reasoning_cfg, dict):
+                if reasoning_cfg.get("enabled") is False:
+                    # Reasoning explicitly disabled — do not set reasoning
+                    # or include.  The Codex backend still thinks by
+                    # default, but we honor the caller's intent where the
+                    # API allows it.
+                    pass
+                else:
+                    effort = reasoning_cfg.get("effort", "medium")
+                    # Codex backend rejects "minimal"; clamp to "low" to
+                    # match the main-agent Codex transport behavior.
+                    if effort == "minimal":
+                        effort = "low"
+                    resp_kwargs["reasoning"] = {
+                        "effort": effort,
+                        "summary": "auto",
+                    }
+                    resp_kwargs["include"] = ["reasoning.encrypted_content"]
+
         # Tools support for auxiliary callers (e.g. skills_hub) that pass function schemas
         tools = kwargs.get("tools")
         if tools: