Fix tests for stable images

What does this MR do and why?

Fixes the rules for the single image tests, as discovered in: https://gitlab.com/gitlab-org/gitlab-docs/-/pipelines/870758995

The single image jobs were configured to be added to the Stable Branch Pipelines, but the tests were not. I created a new rules block just for single image tests, so that we can run just single image tests in the stable branch pipelines, we don't need to test all images. We also test the single images in MR pipelines when making changes to dockerfiles, to hopefully catch config changes that affect the single docker images.

I also noticed that the image jobs themselves will try to build and deploy the site, even if compile_prod failed, because of the needs configuration telling just to wait for the test jobs (ex: https://gitlab.com/gitlab-org/gitlab-docs/-/pipelines/871034895). I expanded that to tell the tests to wait for both the tests and compile_prod, so it'll fail faster if compile_prod fails (the image jobs won't attempt to build).

I'll cherry pick this commit into the 16.0 stable branch as well.

Screenshots, screen recordings, or links to review app

These are strongly recommended to assist reviewers and reduce the time to merge your change.

How to set up and validate locally

Numbered steps to set up and validate the change are strongly suggested.

1. Configure a local GitLab Docs environment: https://gitlab.com/gitlab-org/gitlab-docs/-/blob/main/doc/setup.md.

Merge request acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this merge request.

Related to docs.gitlab.com release 16.0 (May, 2023) (#1613 - closed)