Improve the project manager UI

Created by: Calinou

This incorporates many suggestions from #31342.

This also revises the search behavior to be simpler and more efficient:

• Searching will now search in both the project name and path. A project will be displayed if either of these match the search term.
• If the search term contains a "/", the whole path will be used to match the search term. Otherwise, only the last path component will be used.

Props to @mindinsomnia for providing an high-quality mockup on #31342! ❤

Preview

Before

After