ENH: new statistical distribution infrastructure and spinoff features

Hi team,

There is a PR for the new statistical distribution infrastructure, and there are a few PRs for features that grew out of that effort, so I thought I’d announce them together.

There is also a feature-complete private integrator (_tanhsinh) used in the new distribution infrastructure that compares favorably against existing options in integrate, but this may overlap with RFC: Multidimensional (cubature) integration #20252. However, if there is room for a vectorized, array API compatible function for scalar or vector-valued quadrature in one dimension, possibly with methods to replace the recently-removed romberg and quadrature, I’d be happy to make a PR out of that, too.

Feedback about these features and the API additions is welcome here or in the corresponding PRs. Thanks!