Resolve "Make project and features visibility settings less confusing"

What does this MR do?

Replaces the "sharing and permissions" project dynamic settings panel with one rendered by Vue, eliminating a lot of ~"technical debt" and improving the UX to make it far less confusing.

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

It's the first Vue component that I've written from scratch, so a Vue expert should look it over.

Why was this MR needed?

UX bugs, UI polish, and ~"technical debt"

Screenshots (if relevant)

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• Tests added for this feature/bug
• Review
  • Has been reviewed by UX
  • Has been reviewed by Frontend
  • Has been reviewed by Backend
• Conform by the merge request performance guides
• Conform by the style guides
• Squashed related commits together

What are the relevant issue numbers?

Closes #32665 (closed)