Ubuntu 20.04 Python 3.10 pip import error

I solved exactly the same symptoms by entering pipenv shell and installing pip there:

pipenv shell
curl -sS https://bootstrap.pypa.io/get-pip.py | python

This resulted in:

Collecting pip
  Using cached pip-21.3.1-py3-none-any.whl (1.7 MB)
Installing collected packages: pip
  Attempting uninstall: pip
    Found existing installation: pip 20.0.2
    Uninstalling pip-20.0.2:
      Successfully uninstalled pip-20.0.2
Successfully installed pip-21.3.1

After that things started to work as expected and pipenv install was successful. Countless other ways of installing and reinstalling python/pip/pipenv failed, many times with the same import error.