feat(api): sync test API (serve) + opt-in LLM correction + cloudflared tunnel

- api/: FastAPI app, X-API-Key 인증(미설정 시 임시키), 엔진 load-once 풀
  (+transcribe lock), POST /v1/transcribe(multipart, 동기), /health, /v1/system,
  /v1/models. 업로드 임시파일 finally 삭제(프라이버시).
- postprocess/: llm.correct(scripts/llm_correct.py 승격; opt-in·allowlist·감사로그·재시도)
  + rules.normalize(EmbeddingGemma 등 정규화).
- results/formats.py: txt/srt/vtt. connectivity/tunnel.py: cloudflared quick tunnel(Colab).
- cli serve: uvicorn 단일워커 + --tunnel cloudflare; config llm_* 필드;
  pyproject api/queue extra 분리(+python-multipart, dev httpx).

검증: 22 단위테스트(API TestClient·formats·postprocess) + 실서버 e2e
(/health·auth 401·실제 전사(JFK)·SRT·임시파일 삭제). KO 품질은 turbo/large-v3 필요(tiny는 한국어 degenerate).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

tests/test_api.py

@@ -0,0 +1,86 @@
+"""API — FastAPI TestClient. 엔진은 monkeypatch(가짜)로 모델 로드 회피."""
+from __future__ import annotations
+
+from types import SimpleNamespace
+
+import pytest
+from fastapi.testclient import TestClient
+
+import luke_scribe.api.routes.transcribe as route
+from luke_scribe.api.app import create_app
+from luke_scribe.config import settings
+
+
+class _FakeSeg:
+    def __init__(self, start: float, end: float, text: str) -> None:
+        self.start = start
+        self.end = end
+        self.text = text
+
+
+class _FakeEngine:
+    def transcribe(self, _audio, **_kw):
+        return [_FakeSeg(0.0, 1.0, "안녕 vLLM"), _FakeSeg(1.0, 2.0, "두번째")], SimpleNamespace(
+            language="ko"
+        )
+
+
+@pytest.fixture
+def client(monkeypatch):
+    monkeypatch.setattr(route, "get_engine", lambda *a, **k: _FakeEngine())
+    monkeypatch.setattr(
+        route, "probe_media", lambda p: SimpleNamespace(path=p, duration_s=2.0, size_bytes=1234)
+    )
+    monkeypatch.setattr(settings, "api_keys", ["testkey"])
+    return TestClient(create_app())
+
+
+def _files():
+    return {"file": ("a.wav", b"RIFF0000WAVE", "audio/wav")}
+
+
+def test_health(client):
+    assert client.get("/health").json() == {"status": "ok"}
+
+
+def test_requires_key(client):
+    assert client.post("/v1/transcribe", files=_files()).status_code == 401
+
+
+def test_transcribe_ok(client):
+    r = client.post(
+        "/v1/transcribe", files=_files(), headers={"X-API-Key": "testkey"}, data={"language": "ko"}
+    )
+    assert r.status_code == 200
+    body = r.json()
+    assert body["segments"][0]["text"] == "안녕 vLLM"
+    assert body["model_used"]
+    assert body["corrected"] is False
+
+
+def test_413(client, monkeypatch):
+    monkeypatch.setattr(
+        route, "probe_media", lambda p: SimpleNamespace(path=p, duration_s=999999, size_bytes=1)
+    )
+    r = client.post("/v1/transcribe", files=_files(), headers={"X-API-Key": "testkey"})
+    assert r.status_code == 413
+
+
+def test_srt_format(client):
+    r = client.post(
+        "/v1/transcribe",
+        files=_files(),
+        headers={"X-API-Key": "testkey"},
+        data={"response_format": "srt"},
+    )
+    assert r.status_code == 200
+    assert "00:00:00,000 --> 00:00:01,000" in r.text
+
+
+def test_correct_path(client, monkeypatch):
+    monkeypatch.setattr(route.llm_correct, "correct", lambda text, **k: text + " [보정]")
+    r = client.post(
+        "/v1/transcribe", files=_files(), headers={"X-API-Key": "testkey"}, data={"correct": "true"}
+    )
+    assert r.status_code == 200
+    assert r.json()["corrected"] is True