I had the impression that hash routing in React was deprecated and a React-based back end is almost a mandate now... Wondering what options people are actually taking?
Not at all mandated. Buying into React server-side rendering will get you into a morass of complexity. Traditional SPAs with history-based routing still work just fine.
I've never used SSR and i have quite a few react apps under my belt. Why would you need to introduce it as a full stack app?
I've been using react-router for almost a decade without any issue. I deploy the apps as static websites on S3.
That's not a React thing, but a React Router thing.