How about simply removing the rows with missing y and then design your model and infer the missing y values from that model? I would argue that is even better than using mice :) When using mice this paper could help you but I really don’t see a need for mice if you follow a principle Bayesian way:
@richard_mcelreath in Chapter 15(?) of his 2nd edition book Statistical Rethinking discusses the pros and cons of the approaches. In short, we used multiple imputation approaches when Bayesian imputation was infeasible because we didn’t have computation power.