Problem solved(basically).
The issue seems to involve packages installed/uninstalled by the psychopy conda installer. If I create a fresh environment with Python 3.6.13, and then install tobii-research with pip install tobii-research, all is well. I can import tobii_research as tr, and find all eyetrackers with tr.find_all_eyetrackers().
However, if I first create a conda environment using the installer provided by psychopy – conda env create -n psychopy -f psychopy-env.yml, and then use pip install tobii-research, I recreate my problem importing tobii_research.
I suspect this has something to do with the fact that psychopy uses cached websocket_client-1.0.1-py2.py3-none-any.whl and uninstalled my websocket-client-0.57.0. But, I don’t really know.