The $\mathbb{C}$ vector space monad on the 2-Category of Groupoids

Question

In this post, I am asking about the existence of something called the "Vector Space Monad" on the 2-Category of groupoids (Grpd). In a comment, it was pointed out that the monad should exist due to the properties of Grpd. I am wondering if it is possible to choose a semiring like $\mathbb{C}$, the complex numbers. If so, I am hoping that someone would like to describe this monad on Grpd, for instance how does the functor work, how do the natural transformations work. Jacob's 2013 paper does this for sets.