I did my PhD 2004-2007. I'm not sure whether it was the subject (pure math), my particular advisor or just being two decades ago but I was never aware of any pressure to "publish or perish". I didn't end up continuing in academia post-PhD, but my advisor certainly wanted me to do so, so would have demanded more publication if that was necessary. I'm thankful that I was able to just focus on the quality of research (type I science) and publish when it made sense.

Having said that, I now work in industry research and frequently find myself having to remember and remind others (particularly junior researchers) not to fight the system of industry research too hard if they want to actually get anyone to take notice of their research.