Search (general): either searched value should be kept after search input is reopened, or search should be re-executed after it is closed

[daivabrazukaite]

Current behavior: open for example pages list from site settings -> click on search icon: search input will appear. Enter some text into search input -> enter: filtered pages list will be presented (ok) -> click on search icon: input will disappear, same filtered results list will be left. Click on search icon once more: empty input will appear, but still same filtered list be presented.
So, as reopening search input clears it value, results list should react to available search value or reopening should not clear search value