Stan is probably the most mature, stable PPL, and it's an extremely popular tool, although it isn't really deep-learning-adjacent so gets much less hype.
It's generally used more for modeling and prediction than for creating "products", if that makes sense. More popular among people with statistics or social science backgrounds than among programmers and computer scientists.
If you dig around Stan-related websites you can see various companies and institutions that use it. One I found quite quickly was Metrum Research Group, which does consulting work for the pharmaceutical industry.