So if you're getting your PyPy through your distribution, we're looking at 3-4 versions lag in total.

PyPy claims to be compatible with CPython 3.6.9 (https://www.pypy.org/compat.html). CPython 3.7 is currently the most common Python version. The project I work on since last year depends on features introduced in CPython 3.7. The migration to CPython 3.8 in already underway on many Linux distros (Fedora is already on it). So PyPy is unfortunately too far behind.