In the docs, I read

To transform more than a single vector the preferred representations are rotation matrices, while for other usages Quaternion is the representation of choice as they are compact, fast and stable.

Can you expand on that? Specifically, if the quaternion rotation is faster and cheaper, how would batch rotating an assembly of vectors change anything to that conclusion?

This is because you have to add the cost of the quaternion to matrix conversion.

I don't get it: you first convert quaternions to rotation matrices and then apply them to a vector?

Let's say you have a quaternion and want to apply it to N vectors. The two options are:

1 - performs N quaternion * vector products
2 - convert the quaternion to a 3x3 matrix and performs N matrix * vector products

If N=1, then option 1 is best, otherwise option 2 is better. (I'm not 100% sure for N=2)