find another approach for the "hide the search component"

[12rambau]

The "Hide the search" component is only available when you click on a search link and allow you to remove all the "target" marked in the page. Historically it was in the secondary sidebar but it has some drawbacks. As the element was still there (but simply not visible) it was impossible to remove the secondary sidebar with an "empty" test. it was first introduced in https://github.com/pydata/pydata-sphinx-theme/pull/925 and @choldgraf solved it in another one (I didn't find it bakc sorry).

Now with the new look & fill of the theme I think the button is a bit off as it is non-centered, huge and not ideally placed if the content of the anchor is not at the very top of the page.

I was thinking about an overlay in the bottom right side (like the RDT flyout) which would work on any device and would be easy to spot.

pinging @trallard and @gabalafou as you are our display magicians now !