Search tab is not cleared when selecting a new list

Do a search in any list: the search tabe appears
Select a tab for any list: the search tab remains, as does the search text in the box.
It seems to be necessary to reload the page to clear the search.

No file or test is named. Reproduce the search and list-selection steps described in the issue, then trace the list and search-tab entry points to find where selection state is retained. Done means selecting another list removes the search tab and clears the search text without requiring a page reload.

Written by the indexing model from the issue text.