I guess what do you mean by “super accurate”? The error bars in the plot you posted are quite wide.
The usual tools apply for model validation: posterior predictive checks and whatnot. PSIS-LOO is also still valid-ish, see here. I tried to implement a time-series LOO here, but I never finished it. Help wanted!
If your model isn’t too large, more traditional cross-validation adapted to time series data – sliding window or expanding window – are good. Scikit-learn has tools for doing that. That’s equivalent to making a “porcupine plot” like I show in this notebook. This is an example of “dynamic forecasting”, which is just rolling the transition equation forward from a fixed point, and compute the cumulative error. Here’s a statsmodels example.
Note that my porcupine plot is fake in the sense that I don’t re-fit the model before making each forecast trajectory, so there is data leakage. This is also true if you compute the LOO using az.loo or az.compare, but these can still be useful quantities for model comparison, as the LOO FAQ link above notes.