Your refrigerator's humidity-controlled drawer is the ideal place to store your vegetables, but you might not be using the setting right. The Kitchn gives a simple mantra to get it right: Rot-low, wilt-high.
As the site explains, it's a general rule of thumb where vegetables that will rot should be stored in a drawer with low humidity setting and things that wilt should be stored in a drawer with high humidity.
The general rule of thumb is to put things that rot in a drawer with a low humidity setting. This means veggies that, as you may know from experience, emit an ethylene gas or are sensitive to the gas, like strawberries, avocados, and tomatoes. Leaving the window open on the drawer by choosing the low humidity setting gives those gases a chance to escape and keeps the fruits and vegetables from rotting prematurely.
Things that wilt go in the high humidity drawer. This will be all your leafy greens like arugula, spinach, and basil. By having the window closed water vapor is held in the drawer and the moisture keeps the greens crisper and fresher longer. And a tip like this one will help extend the life of those greens even further.
The full post at The Kitchn includes a list of types of vegetables and the appropriate humidity setting for them: low, medium or high. You could print them out as labels and stick them outside your humidity drawers so there's a ready reference.