An excellent comment, but I would stress that topic models such as LDA and stm are not ordinary clustering methods. They are latent variable models where documents represent a mixture of latent topics.
Sorry if I didn't make that clear: I wasn't saying they are methodically equivalent (although there are similarities, e.g., the Dirichlet Process is a distribution over multinomials, which would be one way to formulate a clustering problem) but that the results can be equivalent, as the cited paper shows.
Down at the bottom, it’s just Gibbs sampling iirc. A distribution of distributions of Gibbs sampling