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_beat_detect_ioi.py

@@ -26,3 +26,14 @@ def test_resolve_bpm_prefers_intervals_over_wrong_aubio():
     bpm = _resolve_bpm(times, 70.0)
     assert bpm is not None
     assert abs(bpm - 120.0) < 5.0
+
+
+def test_resolve_bpm_clamps_runaway_aubio():
+    times = deque([0.0])
+    assert _resolve_bpm(times, 400.0) == 200.0
+    assert _resolve_bpm(times, 999.0) == 200.0
+
+
+def test_resolve_bpm_clamps_slow_aubio():
+    times = deque([0.0])
+    assert _resolve_bpm(times, 30.0) == 60.0