Add an example for pipeline processing

What does this MR do?

Related issues/MRs => #31264 (closed), !53476 (merged), #321972 (closed)

I add this example based on this comment:

we got a customer stating the following:

Sometime in the past 12 hours, my manual jobs started skipping and our pipeline is attempting to deploy to our production environment whenever we merge to master.

Our normal process is to deploy to our dev environment, then manual to QA and manual to production. All manual steps on our pipeline are being skipped. There are also no lines shown connecting the jobs in the pipeline

How can we make sure this change is not related to their issue? They did not change anything in their CI job and the time they are referring to is about the time when we enabled the feature flag.

(BTW, the commented FF rollout issue is not related to this)

Screenshots (strongly suggested)

Example CI file:

stages: [build, test, post_test, deploy]

build:
  stage: build
  script: exit 0

test:
  stage: test
  script: exit 0
  when: manual

post_test:
  stage: post_test
  script: exit 0
  needs: [test]

deploy:
  stage: deploy
  script: exit 0

Before enabling ci_fix_pipeline_status_for_dag_needs_manual

After enabling ci_fix_pipeline_status_for_dag_needs_manual

What happened?

We fixed the infinite "running" status, but we caused "deploy" to run.

Does this MR meet the acceptance criteria?

Conformity

• 📋 Does this MR need a changelog?
  • I have included a changelog entry.
  • I have not included a changelog entry because _____.
• Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides
• Database guides
• Separation of EE specific content

Availability and Testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.
• Tested in all supported browsers
• Informed Infrastructure department of a default or new setting change, if applicable per definition of done

Security

If this MR contains changes to processing or storing of credentials or tokens, authorization and authentication methods and other items described in the security review guidelines:

• Label as security and @ mention @gitlab-com/gl-security/appsec
• The MR includes necessary changes to maintain consistency between UI, API, email, or other methods
• Security reports checked/validated by a reviewer from the AppSec team