Hierarchical Logistic Regression with Binomial Likelihood - The chain reached the maximum tree depth, The rhat statistic is larger than 1.05 for some parameters, The estimated number of effective samples is smaller than 200 for some parameters

Without actually digging into your model, I might suggest reducing the target_accept and increasing the number of tuning steps (using the tune argument). Hitting the max tree depth suggests sub-optimal step sizes (set during tuning) which is going to be exacerbated by asking for very high acceptance rates. Your posterior could definitely be “difficult” and cause these problems on its own, but I would try the easy tweaks first.