feat(06-02): add feature extraction and segmentation backend modules + API

- Create lightsync/audio/features.py with extract_features and extract_features_async
- Create lightsync/audio/segments.py with detect_segments via agglomerative clustering
- Add /api/audio/segments and /api/audio/features endpoints to audio.py
- Initialize app.state.segments cache in main.py lifespan

lightsync/audio/features.py

@@ -0,0 +1,78 @@
+"""Audio feature extraction: onsets, chroma, RMS energy (Phase 6).
+
+extract_features(path) -> {
+    "onset_times": [float, ...],
+    "rms_1s": [float, ...],
+    "chroma_1s": [int, ...],
+    "duration": float,
+    "sr": int,
+}
+"""
+from __future__ import annotations
+import asyncio
+from pathlib import Path
+from typing import Any
+
+
+def extract_features(path: str) -> dict[str, Any]:
+    """Extract onsets, chroma, RMS from audio file.
+
+    Args:
+        path: Absolute path to audio file.
+
+    Returns:
+        Dictionary with onset_times (seconds), rms_1s (per-second mean RMS),
+        chroma_1s (per-second dominant pitch class 0-11), duration, sr.
+    """
+    import librosa
+    import numpy as np
+
+    p = Path(path)
+    if not p.exists():
+        raise FileNotFoundError(f"Audio file not found: {path}")
+
+    y, sr = librosa.load(path, sr=None, mono=True)
+
+    # Onsets — note attacks / transients
+    onset_frames = librosa.onset.onset_detect(y=y, sr=sr, units='frames')
+    onset_times = librosa.frames_to_time(onset_frames, sr=sr).tolist()
+
+    # Chroma — tonal/harmonic content (CQT-based)
+    chroma = librosa.feature.chroma_cqt(y=y, sr=sr)  # shape (12, T)
+
+    # RMS energy — loudness envelope
+    rms = librosa.feature.rms(y=y)[0]  # shape (T,)
+
+    # Reduce to 1s resolution for downstream consumers (heuristic + LLM)
+    hop_length = 512
+    frame_rate = sr / hop_length
+    duration = len(y) / sr
+
+    n_seconds = int(duration)
+    rms_1s = []
+    chroma_1s = []
+    for i in range(n_seconds):
+        start_frame = int(i * frame_rate)
+        end_frame = int((i + 1) * frame_rate)
+        # RMS mean for this second
+        rms_slice = rms[start_frame:min(end_frame, len(rms))]
+        rms_1s.append(float(np.mean(rms_slice)) if len(rms_slice) > 0 else 0.0)
+        # Dominant pitch class for this second
+        chroma_slice = chroma[:, start_frame:min(end_frame, chroma.shape[1])]
+        if chroma_slice.shape[1] > 0:
+            chroma_1s.append(int(np.argmax(np.mean(chroma_slice, axis=1))))
+        else:
+            chroma_1s.append(0)
+
+    return {
+        "onset_times": onset_times,
+        "rms_1s": rms_1s,
+        "chroma_1s": chroma_1s,
+        "duration": duration,
+        "sr": sr,
+    }
+
+
+async def extract_features_async(path: str) -> dict[str, Any]:
+    """Async wrapper — runs in thread pool."""
+    return await asyncio.to_thread(extract_features, path)