Allow multivariate distributions to take in matrices

Description

Looking at the Stan docs we only accept arrays of vectors and row vectors for the multivariate distributions. What do folks think about allowing matrices as well?

We could restrict the current signatures to accept std::vector<Template> and then add a version that accepts matrices of size ([N, M], [N, M], [M, M]).

Example

This would allow for things in Stan like

data {
 int N;
 int M;
 matrix[N, M] Y;
}

parameters {
  matrix[N, M] Mu;
  matrix[M, M] Sigma;
}

model {
 Y ~ multi_normal(Mu, Sigma);
}

I would personally find this useful for time series models where Y is a matrix of time series and Mu is made in transformed parameters and does the VAR component.

Expected Output

All multivariate distributions support matrix inputs

Current Version:

v4.1.0

Start with the current signature in stan/math/prim/prob/multi_normal_lpdf.hpp and review the linked Stan documentation for the existing multivariate distribution inputs. Determine the affected distributions and tests, then verify that all multivariate distributions support the proposed matrix inputs.