What kind of white bean does this recipe take?

As Nancy you both mentioned, I'm sure this soup would work with multiple types of beans - you can use your own intuition and creativity and pick between the options out there, and still make this soup.

As it's not stated, any kind.
Most often meant and used is the whit bean called navy or pea bean.
But use whatever you can get, or best recommended from a store that sells in bulk and has frequent turnover of product.