Originally I had the character waking up around 4 rocks so it was impossible to not move one. But I thought that looked off, so I removed 3 of them, hoping that players would bump into it to see that you can move them and have an ah-hah moment. So that's partially on me for not designing it in a way that made sense or forced the interaction.
The transition effect is a couple of different things working together. Firstly, it's not really a cube. The transition is just taking screenshots of the current and next level, placing them on a quad, positioning those quads to represent a cube rotation, and rotating it.
As for positioning the player on the next level, I made a node called Door, which represents a way to get from screen to screen and it's just an Area2D with a player spawn Marker2D, but it has two variables that controls where to take the player (level and direction - left, right, up, down). This allows me to find the doors on the next level and position the player at the door which points to the level they came from.
Send me a msg on discord if you'd like some more information. Thanks for playing and commenting!