`pip list --quiet` squelches normal output

Environment

• pip version: 20.1.1
• Python version: Python 2.7/3.8
• OS: Arch Linux

Description
When running pip list --quiet or pip list --quiet --quiet, normal output is suppressed, not just warnings. This differs from the behavior of pip freeze (which I am switching from as advised in https://github.com/pypa/pip/issues/8174#issuecomment-621649797).

Expected behavior
Package listing is output, but no warnings.

Actual behavior
With --quiet, only warnings are output. With --quiet --quiet, nothing is output.

How to Reproduce

• Run in Python 2 so that you get the deprecation notice. (This is not necessary, but illustrates better what's happening.)
• Have a few packages installed.

See below for commands to try.

Output

$ pip2 list --format=freeze
DEPRECATION: Python 2.7 reached the end of its life on January 1st, 2020. Please upgrade your Python as Python 2.7 is no longer maintained. pip 21.0 will drop support for Python 2.7 in January 2021. More details about Python 2 support in pip, can be found at https://pip.pypa.io/en/latest/development/release-process/#python-2-support
appdirs==1.4.4
[…]
$ pip2 list --format=freeze --quiet
DEPRECATION: Python 2.7 reached the end of its life on January 1st, 2020. Please upgrade your Python as Python 2.7 is no longer maintained. pip 21.0 will drop support for Python 2.7 in January 2021. More details about Python 2 support in pip, can be found at https://pip.pypa.io/en/latest/development/release-process/#python-2-support
$ pip2 list --format=freeze --quiet --quiet

For comparison:

$ pip2 freeze                       
DEPRECATION: Python 2.7 reached the end of its life on January 1st, 2020. Please upgrade your Python as Python 2.7 is no longer maintained. pip 21.0 will drop support for Python 2.7 in January 2021. More details about Python 2 support in pip, can be found at https://pip.pypa.io/en/latest/development/release-process/#python-2-support
appdirs==1.4.4
[…]
$ pip2 freeze --quiet
DEPRECATION: Python 2.7 reached the end of its life on January 1st, 2020. Please upgrade your Python as Python 2.7 is no longer maintained. pip 21.0 will drop support for Python 2.7 in January 2021. More details about Python 2 support in pip, can be found at https://pip.pypa.io/en/latest/development/release-process/#python-2-support
-f https://leifarne%40auka.io:8YxwbRIe4MAlV5XtXBGVVRY68DWb4S2Rc4x1qNeO6vA@auka-build-tools.appspot.com/find-links
appdirs==1.4.4
[…]
$ pip2 freeze --quiet --quiet
appdirs==1.4.4
[…]

Start by reproducing the reported pip list --quiet and pip freeze --quiet commands with installed packages, comparing normal output and warnings across one and two --quiet flags. Trace the CLI handling for these options and add coverage for the expected package listing and warning behavior; done means pip list retains its package output while suppressing warnings as intended.