refactor(api): complete fastapi migration and related features

Finish native FastAPI controllers, drop vendored microdot, and add
Wi-Fi driver runtime, beat SSE, simulated BPM, sequence playback
improvements, bridge ESP-NOW sources, UI updates, and tests.

Co-authored-by: Cursor <cursoragent@cursor.com>

tests/test_bpm_limits.py

@@ -0,0 +1,45 @@
+"""BPM clamp helpers."""
+
+import os
+import sys
+
+PROJECT_ROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
+SRC_PATH = os.path.join(PROJECT_ROOT, "src")
+if SRC_PATH not in sys.path:
+    sys.path.insert(0, SRC_PATH)
+
+from util.audio_detector import AudioBeatDetector  # noqa: E402
+from util.bpm_limits import (
+    BPM_MAX,
+    BPM_MIN,
+    clamp_bpm,
+    clamp_bpm_optional,
+    max_beat_interval_s,
+    max_beat_min_ioi_ms,
+    min_beat_interval_s,
+)
+
+
+def test_clamp_bpm_bounds():
+    assert clamp_bpm(120) == 120.0
+    assert clamp_bpm(400) == float(BPM_MAX)
+    assert clamp_bpm(20) == float(BPM_MIN)
+
+
+def test_clamp_bpm_optional():
+    assert clamp_bpm_optional(None) is None
+    assert clamp_bpm_optional(0) is None
+    assert clamp_bpm_optional(350) == float(BPM_MAX)
+
+
+def test_beat_interval_bounds():
+    assert abs(min_beat_interval_s() - 60.0 / BPM_MAX) < 1e-9
+    assert abs(max_beat_interval_s() - 60.0 / BPM_MIN) < 1e-9
+    assert abs(max_beat_min_ioi_ms() - 60_000.0 / BPM_MAX) < 1e-6
+
+
+def test_status_clamps_high_bpm():
+    det = AudioBeatDetector()
+    with det._lock:
+        det._status["bpm"] = 350.0
+    assert det.status()["bpm"] == float(BPM_MAX)