I read this over a few times and am having trouble understanding the workflow you are trying to achieve. PBIs are Pending Backlog Items?

I think where you are going wrong is that you are saying Tasks or Backlog Items should map to CI/CD statuses. This is not always the case. Depending on the actual task (or feature) you may not always have a status in your CI/CD pipeline.

The "Done" state of a task is something I've had conversations about in many organizations as they try to mature their processes. In many cases it needs to be broke out more (waiting for QA / done but waiting for internal verification / etc).