Improve the search drop-down menu

[dtdesign]

The search drop-down is largely unmodified since the early days and does not take advantage of newer features.

• [ ] Show tips on how to use the search, such as basic operators (+, - and "…").
• [ ] Easier selection of the search scope.
• [ ] Direct link to the extended search form.
• [ ] Suggest keywords that match the current text input.
• [ ] Show live results for the current search query. (Possibly requires Elasticsearch due to the performance impact?)
• [ ] The behavior for selecting keywords from the list is quirky.