We have many styles related to the layout and visibility of search that
are only useful in the context of the main header. Since many of these
elements have classes that will also be in the sticky header, we should
scope these rules to the main header so that we avoid an uphill battle
of styles trying to override eachother.
Additional changes:
* We previously had a mix of #p-search and .vector-search-box selectors
for the same element in the CSS. Header.less now only uses
.vector-searchbox to avoid specificity wars.
* Removed nearly all of the #p-search rules previously found on L147 -
L167 in screen.less after observing nothing relatively bad happening
when they were removed.
Bug: T289724
Change-Id: I2e6c269e29717cd20d8acfaddc3631ea1b8fedfa