Really cool idea. The art is lovely and the music and lights are really good for getting into a rhythm. I ended up relying on the strategy of only moving on normal and opposite controls beats. I was really surprised by the large amount of levels! I don't think I got to the end, but I did meet the turn-the-world-upside-down thing pretty far into the game.
Level design is solid, but the parts where you have to jump on a spot where the ceiling is too low is too unforgiving (thinking of the level where you meet that upside down thing). Some horizontal jumps use the fact that you can stand a bit into the air when on an edge to make the jump, this is a bit punishing in the earlier levels.
That level in particular (with the jumps in the air where if you fall you get close to the beginning) seems really unforgiving, I'd say the main mechanic on its own is quite challenging; I'd add a few more "easy levels" at the beginning to get the players used to the mechanic.
I had lots of fun, it felt enjoyably confusing, and there was so much content. I really liked it, great job!