This is a followup to #25009, and also resolves the bugs mentioned in #24960.

Here is my attempt (WIP) to create such a package:
https://github.com/dimpase/primecountpy

On PyPI: https://pypi.org/project/primecountpy/

Depends on #25009

CC: @mkoeppe

Component: packages: standard

Author: Dima Pasechnik

Branch/Commit: 74b3845

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/32894