So why didn't anxiety, depression and PTSD abound in historical societies that were always at risk of some bad thing (usually famine but also sometimes invasion)?

Bad stuff has always happened and always will happen. Something about modern society makes us bad at dealing with it in a healthy way.

I don't doubt that there might be some mismatch between the environment our biology is optimized for and the one we live in now but it seems like these conditions weren't common, or if they were they weren't a problem, among our ancestors who lived under different circumstances.