Use multiple runners for multi-architecture builds

- Switch to the Docker metadata action for putting together tags for the
  build-push action. Add more tags, because it's easy now.

- Fold the jobs for the testing and dev containers into the one for the
  server containers. The code duplication is not worth the maintenance cost.

- Clean up names so that they're readable in GitHub's web interface.

- Change how we interact with the GitHub Actions cache for Docker's build
  cache and the GitHub workspace so that the workflow is more resilient to
  being re-run (e.g., for flakey tests, transient errors, etc.)

Author: brianaydemir