Backend: Refactor the status calculation for builds/stages/pipelines

Summary

Before doing a spike (#393013 (closed)) for separating the manual and delayed keyword from when, we need refactoring for the status calculation for builds/stages/pipelines.

Technical details for the current system (WIP): #389276 (comment 1290328736)

Additional details

Some relevant technical details, if applicable, such as:

• Does this need a feature flag?
• Is there an example response showing the data structure that should be returned (new endpoints only)?
• What permissions should be used?
• Is this EE or CE?
  • EE
  • CE
• Additional comments:

Implementation Table

Group	Issue Link
backend	👈 You are here
spike	#393013 (closed)

Links/References