Update TW chores jobs

The TW chores jobs are failing, likely due to a problem with the docker image.

Resolves: #1062 (closed)

• Updates the whitespace task to use .yml format.
• Updates the script for both tasks to support the new structure of the docs site.
  • Demo of working whitespace job: https://gitlab.com/gitlab-org/gitlab-docs/-/jobs/1468987711
  • Demo of unlinked images job: https://gitlab.com/gitlab-org/gitlab-docs/-/jobs/1468952213

During testing I added rules: -if: $CI_PIPELINE_SOURCE == "merge_request_event" so that I could see the results in the pipeline (see above). I've removed that line and reverted the rules, so it'll continue to only run in the chores pipeline.