Update version bump template with new scheduled pipeline

What does this MR do and why?

With recent changes to the structure of pipelines, we can update our template to use the new structure.

For example: https://gitlab.com/gitlab-org/gitlab-docs/-/pipelines/805043914.

I also noticed we hadn't yet mentioned: https://gitlab.com/gitlab-org/gitlab-docs/-/blob/main/.gitlab/ci/rules.gitlab-ci.yml.

CC @axil

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