We attempted to build gevent in evergreen in https://github.com/mongodb/mongo-python-driver/pull/1069 but ran into build errors.

I was able to create an ubuntu-2004-small host, install Python 3.11 from the official Python repository, and install gevent, so it should be possible to do it in our builds as well.  We may need to create a new virtual environment to install gevent using pip.