Cleanup unused typedefs

[andrjohns]

Description

There are a few stray typedefs in the math library that cause compiler warnings, would be good to clean them up

Example

./stan/math/prim/prob/skew_double_exponential_lpdf.hpp: In function ‘stan::return_type_t<T_y0, T_param, T_t0, T_ts> stan::math::skew_double_exponential_lpdf(const T_y&, const T_loc&, const T_scale&, const T_skewness&)’:
./stan/math/prim/prob/skew_double_exponential_lpdf.hpp:47:9: warning: typedef ‘using T_partials_array = class Eigen::Array<typename stan::partials_return_type<T_y, T_x, T_alpha, T_beta>::type, -1, 1>’ locally defined but not used [-Wunused-local-typedefs]
   47 |   using T_partials_array = Eigen::Array<T_partials_return, Eigen::Dynamic, 1>;
      |         ^~~~~~~~~~~~~~~~

Current Version:

v4.1.0