search-box and find-sidebar: split job logic into a dedicated search context

This introduces a better separation between the UI and search code.

1. It is making it easier to move UI components around, or change their behaviour, without touching the search itself. This helps with implementing the new split view based on the recent mock-ups.
2. It helps to reduce the involvement of the window in keeping track of states.
3. The UI components now expect the search context to be changed later. (except for the window) That simplifies maintaining multiple search context – one per tab context – and plugging those into the UI, as a step into the direction of supporting a tabbed view.