[UX] Convert search to a view.

Part of #1332 (end perhaps #151)...

Now with Views in core, we should explore the idea of taking advantage of it and convert the search to a view with exposed filters.

This would allow people to either directly edit the default Search view in order to tweak it to their liking or clone it and create other search views.

It would also expand the ways of extending it with contrib modules that improve the backend (search API) as well as modules that improve the UI (Views).