Here is how to get to a secret bonus area: (all credit goes to the fellow Steam user Whisker):

Step 1: Interact with books in the library in the following order (this unlocks "Something among the books" achievement):

Step 2: Interact with flowers in the garden in the following order (this unlocks "Blooming Flowers" achievement:
Now return to the central area and a new secret staircase should open ("Down Below"
achievement).