Not sure it fits the theme to a T, but it reminds me of something you'd have to do Mario Odyssey for some strange reason -- was this a mechanic they used in that? :D
I did get it to run just fine, and played all five levels, so well done! :)
iirc mario was mostly just swapping between 2d and 3d worlds and didnt have much interaction beyond pressing a button that changes something in the other world but i could be wrong