ubuntu store system python package in /usr/lib/python3/dist-packages and share it for all python3 versions.

Inside an ubuntu 20.04 container (docker run -ti ubuntu:20.04):

apt-get update
apt-get install software-properties-common
add-apt-repository ppa:deadsnakes/ppa
# Install py39 from deadsnakes repository
apt-get install python3.9
# Install pip from standard ubuntu packages
apt-get install python3-pip

Then you can invoke pip with python3.9 -m pip ..., but be careful, everything with be installed in /usr/lib/python3/dist-packages.

But if all you need is a dockerized version of python3.9, it would be better to use the official python docker image, available with debian or alpine (very light) as a base. Both use a standard lib/pythonx.y/site-packages.

By default these images defines entrypoint to the python interpreter, but you can override why bash or busybox sh (alpine).

Edit for debian

launchpad repositories are build on ubuntu distribution. Using on over distribution can lead in libraries incompatibilities.

In deadsnakes ubuntu/xenial repository, python3.9 requires libssl1.0.0, but debian/buster offer libssl1.1.

The easiest way to get python3.9 in debian / buster is to use the official image (docker run -ti python:3.9-buster). Otherwise, build it ...