What is PP to you? Just any application of bayesian techniques? You should reframe your question in terms of what kinds of problems bayesian techniques are SOTA for and then explore what companies operate in those spaces. No startup is "focusing on" PP, it's not a field where there is significant R&D overhang relative to industrial applications like deep learning has seen the last few years. Nobody is getting VC dollars to research new posterior sampling methods.
There are some areas where it's USEFUL to apply existing techniques, usually contexts where it's useful to have a confidence measurement attached to the prediction. Think big decisions based on small data (not always though). Investing, pharma, etc. STAN is SOTA in many ways but if you're interested in higher throughput inference Variational Inference is the preferred technique and that's best supported by something like PyMC.
