AI providers: review follow-ups to 0060ccd

Replay usage key gemini_usage -> llm_usage (backend + ReplayTab), re-price the
correction/correlation estimates for gpt-4o-mini, no temperature for o-series
or gpt-5 models, and refresh comments still naming Gemini.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

drb-c2-core/app/internal/llm.py

@@ -79,11 +79,15 @@ def generate_json(model: str, prompt: str, *, purpose: str,
     from app.internal.ai_clients import openai_client
     # JSON mode requires the word "JSON" in the prompt; both prompts say
     # "Return JSON" / "Respond with JSON only".
+    kwargs = {}
+    # Reasoning models (o-series, gpt-5) reject a temperature; chat models get 0.
+    if not model.startswith(("o1", "o3", "o4", "gpt-5")):
+        kwargs["temperature"] = 0
     resp = openai_client().chat.completions.create(
         model=model,
         messages=[{"role": "user", "content": prompt}],
         response_format={"type": "json_object"},
-        temperature=0,
+        **kwargs,
     )
     usage = getattr(resp, "usage", None)
     record_usage(purpose, model,