After installing Python 3.9.1 on Windows 10 system-wide to "C:\Program Files\Python39", I tried to pip install the package 'dirsearch'.

pip refused with the error: "Defaulting to user installation because normal site-packages is not writeable", and proceeded to write to Local AppData (unwanted, so I deleted from AppData).

I changed the permissions of the site-packages folder to allow python access (allowed Users and Application Packages full control). 

Then I retried installing 'dirsearch', which now completed successfully. However, I was warned that my pip version was out of date. So I did:
>>> py -m pip install --upgrade pip
I ensured py --version = 3.9.1

This failed with "ERROR: Could not install packages due to an EnvironmentError: [WinError 5] Access is denied: 'c:\\program files\\python39\\scripts\\pip.exe'

I then allowed same permissions as site-packages to the scripts folder. 

Retried 
>>> py -m pip install --upgrade pip
and I get an error:
"C:\Program Files\Python39\python.exe: No module named pip"

I navigate to site-packages, where pip directories have been renamed as:
~ip
~ip-21.0.dist-info

This is better reported at https://github.com/pypa/pip, as it will be fixed out of their repository and then updated into here.

Seems like the failed install did not roll back properly. Those directories are the backup of the uninstallation so that if it fails, they can be restored. It's not obvious why that didn't work here.