Overfitting and model validation in frequentist inference is framed in terms of the frequentist properties of given decisions (which point of interval estimator to report, etc). Consequently these concepts don’t directly carry over to a Bayesian context because Bayesian inference doesn’t enforce any particular decision making processes. In order to formally transfer these ideas over to a Bayesian context you have to establish which decisions you want to make and then how you will use the posterior to inform those decisions, and then you can start asking questions about how well you do.
For more detail on this perspective see https://arxiv.org/abs/1803.08393.