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/vocabulary_learner.py

@@ -470,7 +470,7 @@ def _diff_new_terms(original: str, corrected: str) -> list[str]:
 
 def _sync_bootstrap(system_name: str, system_type: str, area_hint: str) -> list[str]:
     from app.config import settings as cfg
-    from openai import OpenAI
+    from app.internal.ai_clients import openai_client
 
     if not cfg.openai_api_key:
         return []
@@ -481,7 +481,7 @@ def _sync_bootstrap(system_name: str, system_type: str, area_hint: str) -> list[
         area_hint=area_hint,
     )
     try:
-        client = OpenAI(api_key=cfg.openai_api_key)
+        client = openai_client()
         response = client.chat.completions.create(
             model="gpt-4o",
             messages=[{"role": "user", "content": prompt}],
@@ -504,7 +504,7 @@ def _sync_induct(
 ) -> list[dict]:
     """Returns [{term, meaning}] — a bare string is still accepted from the model."""
     from app.config import settings as cfg
-    from openai import OpenAI
+    from app.internal.ai_clients import openai_client
 
     if not cfg.openai_api_key:
         return []
@@ -518,7 +518,7 @@ def _sync_induct(
         transcript_block=transcript_block[:8000],
     )
     try:
-        client = OpenAI(api_key=cfg.openai_api_key)
+        client = openai_client()
         response = client.chat.completions.create(
             model="gpt-4o-mini",
             messages=[{"role": "user", "content": prompt}],