Fix archived parameter for projects API

What does this MR do?

Fixes a regression where the archived parameter is incorrectly applied to the projects finder.

Are there points in the code the reviewer needs to double check?

It changes default (but incorrect per spec) API behavior which is in place for 1,5 years. Currently without archived parameter only active projects are returned (so filter archived=false is incorrectly applied). The current default API behavior matches GUI behavior, however it's not possible to filter archived projects only via API (which is possible via GUI).

This MR replaces !17244 (closed) (from @razer6), which is un-maintained for last 5 months due to contributor inactivity. The code from that MR is refreshed and remaining open comments are implemented.

Why was this MR needed?

See discussions in #32301 (closed) and !17244 (closed)

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• API support added
• Tests added for this feature/bug
• Conform by the code review guidelines
  • Has been reviewed by a UX Designer
  • Has been reviewed by a Frontend maintainer
  • Has been reviewed by a Backend maintainer
  • Has been reviewed by a Database specialist
• Conform by the merge request performance guides
• Conform by the style guides
• Conform by the database guides
• If you have multiple commits, please combine them into a few logically organized commits by squashing them
• Internationalization required/considered
• End-to-end tests pass (package-and-qa manual pipeline job)

What are the relevant issue numbers?

Closes #32301 (closed)