Experiment: automatically push built images

What does this MR do and why?

Describe in detail what your merge request does and why.

• Add image with docker and docker buildx plugin: https://docs.docker.com/buildx/working-with-buildx/
• Use buildx by default to build images (potentially add multiplatform builds -- https://docs.docker.com/buildx/working-with-buildx/#build-multi-platform-images)
• Simplify CI, remove duplication between test/build, push automatically on master pipeline

By adding .dockerignore and optimizing caching, it should be fine to simply run and push all the images automatically since without actual changes, the image is fully cached: https://gitlab.com/gitlab-org/gitlab-build-images/-/jobs/2437434061

Closes #105 (closed)