Remove non-docs jobs from docs pipelines

What does this MR do?

I noticed in a recent docs-only MR that the docs pipeline had multiple jobs that were not related to docs, including one that was blocking the pipeline: https://gitlab.com/gitlab-org/charts/gitlab/-/pipelines/1636651212

This MR:

• Removes the preflight jobs from docs pipelines.
• Removes the PIPELINE_TYPE: "${PIPELINE_TYPE}" in the trigger_operator_test job which was causing the blocking job to be added to the docs pipelines.

Related issues

• Related to Fix broken reviews in DOCS_PIPELINE (!4042 - merged)

Author checklist

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Required

For anything in this list which will not be completed, please provide a reason in the MR discussion.

• Merge Request Title and Description are up to date, accurate, and descriptive.
• MR targeting the appropriate branch.
• MR has a green pipeline.
• Documentation created/updated.
• Tests added/updated, and test plan for scenarios not covered by automated tests.
• Equivalent MR/issue for omnibus-gitlab opened.

Reviewers checklist

• MR has a green pipeline on https://gitlab.com/gitlab-org/charts/gitlab.
• Consider downstream impact to the Operator, as per evaluating impact from changes to GitLab Chart.