This is a stucking bug. If you manage to reach night without doing the second part of the exam, you have no chance to go on.
If you have an older savefile you can easy reload from there.
Or you can save, open this in texteditor, search for "daytime" and change it to "daytime":3 (or1,2), then save this again and reload in game.
You find the saves in windows here.
C:\Users\your_user\AppData\Roaming\Godot\app_userdata\High School of Succubus\saves