Add a CI job that actually builds the Docker images

Problem

Nothing in this repository ever builds the Docker image. The only CI workflow, Gradlew Check, runs
./gradlew and fails if the generated directories differ from the template — it verifies that the
generated files are up to date, never that they produce a working image.

As a result a Dockerfile can be broken on master for weeks and we only find out when the Docker
Official Images pull request is opened, which is the worst possible moment: the release has already been
announced and the fix has to go through a second round trip with the Docker Official Images
maintainers.

XDOCKER-421 is exactly that: ARG TARGETARCH was only populated by BuildKit, so the image failed to
build under the classic builder that the Docker Official Images infrastructure uses. The problem sat on
master for nine days and surfaced only in the 18.6.0 update pull request.

Proposal

Add a CI workflow that actually builds the generated {{Dockerfile}}s and checks the resulting images,
using the same classic builder that the Docker Official Images infrastructure uses, so that this class
of breakage is caught on the pull request instead of at release time.