Draft: Add job to verify and push gitlab e2e tests image

What does this merge request do and why?

Add a job to regularly test and push a gitlab e2e test docker image

Closes #1680 (closed)

This won't be needed once gitlab!117622 (merged) is merged.

How to set up and validate locally

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

Impacted categories

The following categories relate to this merge request:

• gdk-reliability - e.g. When a GDK action fails to complete.
• gdk-usability - e.g. Improvements or suggestions around how the GDK functions.
• gdk-performance - e.g. When a GDK action is slow or times out.

Merge request checklist

• This change is backward compatible. If not, please include steps to communicate to our users.
• Tests added for new functionality. If not, please raise an issue to follow-up.
• Documentation added/updated, if needed.
• Announcement added, if change is notable.
• gdk doctor test added, if needed.
• Add the ~highlight label if this MR should be included in the CHANGELOG.md.