64-bit Python running in 32-bit mode isn't able to install any of aarch64 and armv7l wheels

On a 64-bit Raspberry Pi, sysconfig.get_platform() returns linux_armv8l instead of linux_aarch64 while sys.maxsize is over 32-bit range

root@raspberrypi:~# linux32 python3 -c 'import sysconfig; print(sysconfig.get_platform())'
linux-armv8l
root@raspberrypi:~# linux32 python3 -m pip debug --verbose
WARNING: This command is only meant for debugging. Do not use this with automation for parsing and getting these details, since the output and options of this command may change without notice.
pip version: pip 21.3.1 from /usr/local/lib/python3.8/dist-packages/pip (python 3.8)
sys.version: 3.8.2 (default, Mar 13 2020, 10:14:16)
[GCC 9.2.1 20200306]
sys.executable: /usr/bin/python3
sys.getdefaultencoding: utf-8
sys.getfilesystemencoding: utf-8
locale.getpreferredencoding: UTF-8
sys.platform: linux
sys.implementation:
  name: cpython
'cert' config value: Not specified
REQUESTS_CA_BUNDLE: None
CURL_CA_BUNDLE: None
pip._vendor.certifi.where(): /usr/local/lib/python3.8/dist-packages/pip/_vendor/certifi/cacert.pem
pip._vendor.DEBUNDLED: False
vendored library versions:
  CacheControl==0.12.6
  colorama==0.4.4
  distlib==0.3.3
  distro==1.6.0
  html5lib==1.1
  msgpack==1.0.2 (Unable to locate actual module version, using vendor.txt specified version)
  packaging==21.0
  pep517==0.12.0
  platformdirs==2.4.0
  progress==1.6
  pyparsing==2.4.7
  requests==2.26.0
  certifi==2021.05.30
  chardet==4.0.0
  idna==3.2
  urllib3==1.26.7
  resolvelib==0.8.0
  setuptools==44.0.0 (Unable to locate actual module version, using vendor.txt specified version)
  six==1.16.0
  tenacity==8.0.1 (Unable to locate actual module version, using vendor.txt specified version)
  tomli==1.0.3
  webencodings==0.5.1 (Unable to locate actual module version, using vendor.txt specified version)
Compatible tags: 30
  cp38-cp38-linux_armv8l
  cp38-abi3-linux_armv8l
  cp38-none-linux_armv8l
  cp37-abi3-linux_armv8l
  cp36-abi3-linux_armv8l
  cp35-abi3-linux_armv8l
  cp34-abi3-linux_armv8l
  cp33-abi3-linux_armv8l
  cp32-abi3-linux_armv8l
  py38-none-linux_armv8l
  py3-none-linux_armv8l
  py37-none-linux_armv8l
  py36-none-linux_armv8l
  py35-none-linux_armv8l
  py34-none-linux_armv8l
  py33-none-linux_armv8l
  py32-none-linux_armv8l
  py31-none-linux_armv8l
  py30-none-linux_armv8l
  cp38-none-any
  py38-none-any
  py3-none-any
  py37-none-any
  py36-none-any
  py35-none-any
  py34-none-any
  py33-none-any
  py32-none-any
  py31-none-any
  py30-none-any
root@raspberrypi:~# linux32 python3
Python 3.8.2 (default, Mar 13 2020, 10:14:16)
[GCC 9.2.1 20200306] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import sys
>>> sys.maxsize <= 2 ** 32
False

This makes tests on Alpine Linux's CI fails sometimes, for example https://gitlab.alpinelinux.org/omni/aports/-/jobs/514000 , looks like they're running armv7 and armhf gitlab runners on 64-bit ARM machines in 32 bit mode.

Originally posted in https://github.com/pypa/packaging/pull/234#discussion_r737238107

Start by reproducing the behavior with linux32 python3, checking sysconfig.get_platform(), sys.maxsize, and python3 -m pip debug --verbose on a 64-bit Raspberry Pi. Trace how the linux_armv8l platform value becomes compatible wheel tags, then verify that the resulting tags allow the relevant aarch64 and armv7l wheels without breaking other platforms.