You fit random-effects panel-data or longitudinal models by using xtreg for continuous outcomes, xtlogit or xtprobit for binary outcomes, xtologit or xtoprobit for ordinal outcomes, and more. In Stata 17, you can fit Bayesian versions of these models by simply prefixing them with bayes. See the full list of supported commands in [BAYES] Bayesian estimation under Panel-data models.