I run into this error pretty regularly on macOS after upgrading (or downgrading) MySQL using homebrew. The error message is confusing, because I have installed the mysqlclient Python package—it’s just failing to load properly.
The problem is your pip cache has a mysqlclient built with the wrong MySQL version, and pip keeps reinstalling that.
To fix, force pip to rebuild it ignoring the cache:
pip install --force --no-cache mysqlclient==<version>