I have the generalized_skew_t lpdf and lcdf functions at helpful_stan_functions/skew_generalized_t.stanfunctions at main · spinkney/helpful_stan_functions · GitHub.
These reduce to skew T by setting p = 2. However, it appears that the parameterization is different from the sn R package. Due to the use of lambda which is between -1, 1. The Skew T that it reduces to is the skew T from https://www.ssc.wisc.edu/~bhansen/papers/ier_94.pdf equation 10 (p. 710, pdf p. 6).
I also have the quantile function in that repo for this distribution.