Refactor dockerfile to support Buildkite AND Github Actions (#71954)

This change adds the image used by the self-hosted Github Actions
builders.

In an attempt to make the transition simple, all of the different images
share as much of the same state as possible, including packages, users,
etc... This results in bigger images, but that shouldn't be a problem.
That said, the refactorings caused the buildkite image to shrink by 100
MB.

This change also renames all of the packages for consistency. Bots will
have to be changed to use the new package names eventually.

Again, docker-compose was used as the source of truth for defining
argument.

I have already pushed example images to ghcr.io/libcxx/<name>:testing