fix: split 'cuda:N' into device+device_index for CTranslate2

Colab A100 run exposed a GPU-only bug: DeviceManager returns
selected_device='cuda:0' and the engine passed it verbatim to
faster-whisper, but CTranslate2 only accepts device='cuda' with a
separate device_index arg -> 'unsupported device cuda:0' on every GPU
transcription. Fix: FasterWhisperEngine._split_device() splits
'cuda:N' -> ('cuda', N) and passes device_index to WhisperModel.

Notebook: server cell now pkills stale servers (old process holds
port 8000 and 401s on new keys since KeyStore loads at startup),
sets LUKESCRIBE_API_KEY_FILE explicitly, and verifies auth with
RAW_KEY before proceeding; worker cell guards read_result() is None.

+ 4 unit tests (device split contract), 131 tests pass, ruff clean.

tests/unit/test_engine_faster_whisper.py

@@ -0,0 +1,80 @@
+"""FasterWhisperEngine 단위 테스트 — CTranslate2 호출 계약 (device 분리).
+
+faster-whisper/CTranslate2는 ``device`` 문자열로 "cuda"만 허용하며 인덱스는
+별도 ``device_index`` 인자로 받는다. DeviceManager가 내려주는 "cuda:N"을
+제대로 분리해 전달하는지 mock으로 검증한다 (GPU 환경에서만 재현되는 버그
+— Colab 실전 테스트에서 ``unsupported device cuda:0``으로 확인됨).
+"""
+
+from __future__ import annotations
+
+import sys
+import types
+
+from luke_scribe.engine.base import TranscriptionOptions
+from luke_scribe.engine.faster_whisper_engine import FasterWhisperEngine
+
+
+class FakeWhisperModel:
+    """faster_whisper.WhisperModel 대체 — 생성 인자만 기록한다."""
+
+    calls: list[dict] = []
+
+    def __init__(self, *args, **kwargs) -> None:
+        self.kwargs = kwargs
+        self.__class__.calls.append(kwargs)
+
+    def transcribe(self, audio_path, **kwargs):
+        return iter([]), {}
+
+
+def _install_fake(monkeypatch) -> None:
+    mod = types.ModuleType("faster_whisper")
+    mod.WhisperModel = FakeWhisperModel
+    monkeypatch.setitem(sys.modules, "faster_whisper", mod)
+    FakeWhisperModel.calls.clear()
+
+
+def _opts(**kw) -> TranscriptionOptions:
+    kw.setdefault("model", "large-v3-turbo")
+    kw.setdefault("device", "cuda:0")
+    kw.setdefault("compute_type", "float16")
+    return TranscriptionOptions(**kw)
+
+
+def test_cuda_device_index_split(monkeypatch):
+    """'cuda:0' → device='cuda', device_index=0 (Colab A100 첫 GPU)."""
+    _install_fake(monkeypatch)
+    FasterWhisperEngine().transcribe("/tmp/x.wav", _opts())
+    kwargs = FakeWhisperModel.calls[-1]
+    assert kwargs["device"] == "cuda"
+    assert kwargs["device_index"] == 0
+    assert kwargs["compute_type"] == "float16"
+
+
+def test_cuda_second_device_index(monkeypatch):
+    """'cuda:1' → device='cuda', device_index=1."""
+    _install_fake(monkeypatch)
+    FasterWhisperEngine().transcribe("/tmp/x.wav", _opts(device="cuda:1"))
+    kwargs = FakeWhisperModel.calls[-1]
+    assert kwargs["device"] == "cuda"
+    assert kwargs["device_index"] == 1
+
+
+def test_cpu_passthrough(monkeypatch):
+    """'cpu' → 그대로 device='cpu', device_index=0."""
+    _install_fake(monkeypatch)
+    FasterWhisperEngine().transcribe("/tmp/x.wav", _opts(device="cpu", compute_type="int8"))
+    kwargs = FakeWhisperModel.calls[-1]
+    assert kwargs["device"] == "cpu"
+    assert kwargs["device_index"] == 0
+    assert kwargs["compute_type"] == "int8"
+
+
+def test_split_device_helper():
+    assert FasterWhisperEngine._split_device("cuda:0") == ("cuda", 0)
+    assert FasterWhisperEngine._split_device("cuda:3") == ("cuda", 3)
+    assert FasterWhisperEngine._split_device("cpu") == ("cpu", 0)
+    assert FasterWhisperEngine._split_device("cuda") == ("cuda", 0)
+    # 파싱 불가 인덱스는 그대로 전달 (모델 로드 시 명시적 오류로 fail-explicit)
+    assert FasterWhisperEngine._split_device("cuda:xx") == ("cuda:xx", 0)