I liked your game even if I never got past section 3 in the first level. I do like the music and the carry out with the effects in the game making it a well put together game.
One suggestion is that after calibrating the gamepad it would have been nice if you could navigate the menus with the gamepad. But I also know game jams is a lot of hard prioritizations to get the game done.
I took a peek in the source code and was interesting to see how you made your controllers inherit from Component and HasGameReference to make the inter-controller wiring that way. I've been doing very explicit prop-drilling for inter-state read/writes which has its pros and cons.