I just can't find how to interact with the shopkeeper in the VIP room or what I have to do to be able to buy the courses
It's actually quite easy. First, go to the store. In the bottom right corner, there's a button that says "Action," and there's only one option: "Bronze VIP Card" (this is version 2.2). Once you select that option, a cutscene will start. Then, head to room 001. Once inside, approach the small black table until a "Press E" message appears. The saleswoman will then allow you to purchase the courses. Remember to buy them all to get the Lab 2 manual.