Fully refactored the level manager.
After a few hours, I have finally cleaned up all the code for level transitions. Now, the code is easier to understand and maintain, and adding new levels takes significantly less time and effort. I added comments on all the related code to make it even easier to read.
I also fixed a few bugs in the process. For example, trying to open the menu during a level transition used to put the game in a glitched state, but I fixed that now. I moved towards a cleaner architecture where the scene root (play.tscn) manages the game state, and the pause menu asks the play scene to open the menu, instead of just going ahead and doing it.
It’s possible that this refactor may have broken some other aspects of the game, so I’ll have to look over everything later, but right now, it seems to be working fine.