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.

[TimWolla]

Duplicate of #3393

[eveneme]

The centered menu on the screen in the form of a popup window looks good.

Examples:

Video: https://cdn.dribbble.com/users/4256532/screenshots/16434078/media/ac337571daecd589e39801cf81c7ec39.mp4

[eveneme]

The search bar seems to look the worst compared to the rest; I suggest a complete redesign. A good option would be a popup window with a background blur effect, or simply a sliding design, as seen on Facebook, for example.