Remove test_unlinked_images dependency on lint-html Docker image

What does this MR do and why?

I noticed while working on technical-writing#1042 (closed) that we have a dependency on gitlab-docs/lint-html.

We'd like to eventually not have the gitlab-docs/lint-html at all, so it seems like a good time to remove a dependency on it. It's has meant that the job has to do more heavy lifting itself.

• Before: https://gitlab.com/gitlab-org/gitlab-docs/-/jobs/6998990189
• After: https://gitlab.com/gitlab-org/gitlab-docs/-/jobs/7030995406 (results differ because of: gitlab!155162 (merged)).

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