I can’t think of a specific example, but mostly because I tend to work with ecological data from animals.
@martinmodrak is working on a project like this now, some details of a previous model formulation here: Reanalyzing the Gautret et al. data on Covid-19 treatment. Asking for feedback
@LuisDamiano has a writeup on HMMs in Stan: https://zenodo.org/record/1284341/files/main_pdf.pdf?download=1 as well as an R package that could be helpful, BayesHMM: https://luisdamiano.github.io/BayesHMM/articles/introduction.html#introduction
The Stan manual has examples on how to implement hidden Markov models as well. I know there are various types of HMM formulations applied to longitudinal data, with both discrete- and/or continuous-valued random effects, and these can all be easily incorporated using Stan.