I used to set up environment evariables http_proxy and https_proxy (with user + password) in the past to use Pip (on Windows) behind a corporate proxy. But recently I needed to tell Pip to use a proxy without setting up environment variables as this conflicted with git configuration in combination with SSL Certificates which I get to work only by removing environment variables for proxy.
Fortunately you can configure PIP with an pip.ini file as described here: https://pip.pypa.io/en/stable/user_guide/#config-file
The detailed answer to my own question follows below.