At the risk of contributing my own probably-subtly-broken advice to the collection already present in this thread, I would note that there is a relatively sane system python3 on Catalina/Big Sur, and most projects are building and distributing compatible wheels [1] (binary packages). So something like:
/usr/bin/python3 -m venv ./venv # create a virtual environment in ./venv
./venv/bin/pip install wheel # optional
./venv/bin/pip install dep1 dep2 dep3 ...
./venv/bin/python ... # up and running