[UX] Search block: Provide options to render either as a separate field/button, or as a searchbar

This is a follow-up feature request from #3476.

@BWPanda

Would it be too far of a stretch to convert the blue 'Search' button to a magnifying-glass icon and position it, right-aligned, inside the search box?

@jenlampton

I am in support of this, but it would affect existing sites without supplemental css

@indigoxela

Here's example code from a contrib theme that makes the search box a "search bar".

but it would affect existing sites without supplemental css

Yeah, that's a good point. It could interfere with subthemes of Basis that implemented something similar.

@klonos

We could have a follow-up feature request, to add options to the search block, similar to those that we have for the menu blocks re the menu "style":

Quick mockup :