I have document parsing and SPARQL queries that can take a few minutes that I'd like to run frequently so I can keep all parts of the system up to date.
I've only benchmarked it a bit, but I found I got approximately the five times speed-up that PyPy promised. This is with PyPy based on Python 3.6. I think PyPy is switching to cffi as the way to connect to C code so most native code "just works" now.
I had to backport my code from Python 3.8; Python 3.6 lacks contextvars, but there is a polyfill for that, otherwise there was no problem.
I stayed away from PyPy for a long time because it was tied to Python 3.5 which was busted in various ways. One of those was that the filesystem path objects were half-implemented, you should have been able to pass them into anything from the stdlib that expected a string path and at that time you couldn't. Little accidents like that can slow down a technology like PyPy from being adopted.