I recently did an AR model with student-T innovations using pm.CustomDist on a panel of several thousand timeseries and it fit in a reasonable time (<=1hr). For simple models (e.g. no hidden states) this is where I’d start.
I think Prophet is still a really good general starting point. I go through an implementation here, and there’s also an example notebook. Neither goes into how to do hierarchy, but it’s just y = X\beta, so you’ll just be doing the usual indexing tricks for regression models. If you go that route and get stuck, don’t hesitate to make a thread asking for help.