feat(audio): Complete Phase 3 - Migrate main.cc to AudioEngine (Task #56)

Migrated production code (main.cc) to use AudioEngine instead of directly
calling synth_init() and tracker_init(), eliminating initialization order
dependencies in the demo entry point.

Changes:
- Added #include "audio/audio_engine.h" to main.cc
- Replaced synth_init() + tracker_init() with AudioEngine::init()
- Replaced tracker_update(g_music_time) with g_audio_engine.update(g_music_time)
- Preserved direct synth calls (synth_register_spectrogram, synth_get_output_peak)
  as these are valid API usage

Results:
- All 20 tests pass (100% pass rate)
- Demo runs successfully without crashes
- Initialization order fragility eliminated in production code
- Test suite time: 8.13s (unchanged)

Known Technical Debt (deferred to Phase 4):
- audio_init() still calls synth_init() internally for backwards compatibility
- This causes double initialization (harmless but fragile)
- Some tests rely on this behavior
- Will be cleaned up in Phase 4 with other compatibility shims

handoff(Claude): Completed Task #56 Phase 3 - production code now uses AudioEngine.
Phase 4 (Cleanup) remains: remove old global functions, update remaining tests,
remove backwards compatibility shims, update documentation.

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

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