Use the staging repository for tagging/pushing container images. We
aren't able to (and wouldn't want to) push directly to the production
repository that is the default in the Makefile.
Use make for building our container image (through a new push-image.sh
script) instead of building directly with docker. This way we avoid the
container image tag naming hassle where we build and push the image on
"image-pushing" prow job and need to be able to reliably re-create the
same tag on the "testing" side for end-to-end tests. This also has the
advantage that the same mechanism (make) is used everywhere, i.e. in
image-pushing, testing and locally.