Thank you!! The music lag is a bug I had in other games I've made using p5js too. Until I find a clear evidence that my code is the cause of the problem I'll blame p5js (haha just kidding)
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I found a bug! If you press any key multiple times while loading the game, you can skip 1 level. Also regarding the music lag, it appears to be a p5js issue - https://github.com/processing/p5.js-sound/issues/635