I kinda think it's not the iGPU that is the problem as you said the gameplay itself was smooth. The music processing should be processed by the CPU anyway. Something could be blocking the start of the music or the game tries to restart it every frame.
I have tested with my laptop and mobile phone. They are a bit laggy, but both of them play the music and show the notes for the rhythm.
- Laptop (AMD Ryzen 5 5625U with iGPU)
- Mobile phone (Qualcomm Snapdragon 865 + Adreno 650 GPU)
If you hear the birds, but not the music then it makes me think the issue is AudioStreamSynchronized. I use that for looping the music tracks in sync, but the ambiance uses regular AudioStreams. There's a possibility that Godot 4.6 has a bug in AudioStreamSynchronized that makes it incompatible with your hardware.
Thanks again for helping me figure this out.