Move search field to top bar so it is always visible

I mostly search for specific users to adjust their data, so after editing a user this would save me one click (going back to the frontpage).
Plus apart from four links the top bar is empty so there is enough space.

No files, tests, or entry points are mentioned. Locate the current search field and top-bar template, then check how the front page and user-editing views render them. Done means the search field remains visible in the top bar while editing a user and still performs the existing search.

Written by the indexing model from the issue text.