Explicit timeouts on every OpenAI and Gemini request (#153)

No AI client set a timeout: OpenAI's SDK waits 600s per attempt and retries
twice (timeouts included); google-genai waits forever. A hung provider call
had no upper bound, so recorrelation_sweep's 15-minute pipeline hold-back was
a guess against an unbounded tail.

- config: stt_timeout_seconds (120), openai_timeout_seconds (60),
  openai_max_retries (1), gemini_timeout_seconds (60).
- app/internal/ai_clients.py builds every OpenAI/AsyncOpenAI client with them
  (transcription, extraction, embeddings, summarizer, vocabulary learner,
  trip chat). gemini.py's shared client gets HttpOptions(timeout=ms).
- A timeout raises like any other provider error, so existing fallbacks are
  unchanged: rules-only correlation, rules decision on tiebreak, raw
  transcript on correction, ai_health "transient".
- MIN_MINUTES_SINCE_PIPELINE_START is now derived from those timeouts
  (pipeline_worst_case_seconds, 3-scene budget + 2 min non-AI slack), floor
  15: 21 min with the defaults. Loop warns if it reaches the scan window.
- tests/test_ai_timeouts.py: client limits, a real hung-socket request that
  gives up in <5s, timeout fallback per tier, the derived bound, and a guard
  against any new OpenAI( outside ai_clients.py.

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

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

@@ -44,7 +44,18 @@ def _get_client():
     with _client_lock:
         if _client is None:
             from google import genai  # lazy — only when a Gemini call is made
-            _client = genai.Client(api_key=settings.gemini_api_key)
+            from google.genai import types
+            # server-26#153: google-genai's default is no timeout at all, so a
+            # hung call held its pipeline (and the sweep hold-back sized
+            # against it) open indefinitely. HttpOptions.timeout is in ms.
+            # The client does not retry unless retry_options is set, so this
+            # is the whole bound per request. A timeout raises from
+            # generate_json like any API error, so every caller's fallback
+            # (rules-only correlation, uncorrected transcript) is unchanged.
+            _client = genai.Client(
+                api_key=settings.gemini_api_key,
+                http_options=types.HttpOptions(timeout=int(settings.gemini_timeout_seconds * 1000)),
+            )
         return _client