It’s challenging to find good resources because much of the Bayesian time series literature is focused on inference methods that use more efficient sampling methods like filtering. Those methods scale well to much longer time series (i.e. T >> 100) but typically require writing down a new set of equations for inference every time.
An additional problem is that some of the classical time series / econometrics literature focuses on very specific time series models such as GARCH and ARMA among others without explaining how they’re part of a larger class of dynamic models. This review paper moves quickly and assumes a fair amount of background but it presents a very general framework for thinking about dynamic linear models (DLMs) for time series. DLMs typically include autoregressions and dynamic regressions as special cases. I have not read this paper in detail but it also appears to cover the same material. It’s important to keep in mind that we can be much more flexible with regard to parametric assumptions than these DLM papers since NUTS is a general purpose inference algorithm.
Finally, since PyMC3 and Stan share many similarities, I often use the Stan manual for reference. It has a section on time series data as well.