Window Walker search field should default to empty

### Description of the new feature / enhancement

Currently, whenever you open window walker, by default the search field is auto-populated with the last search history. However, for users who want to primarily use Window Walker to switch between the windows/apps on their desktop, it'd be much better if the search field is empty by default, because then you wouldn't have to backspace to remove the last search history. You could just open window walker and start typing the name of the window you want to switch to right away!

EDIT: I'm sorry I wasn't clear in my previous description. But the search field is pre-filled with last typed characters after you have already used window walker to switch to a window. Please refer the gif below. After I use window walker to switch to brave, and then when I open window walker again, my last typed characters are still there. The search field should be emptied after the user has successfully switched to a window.


### Scenario when this would be used?

In the scenario when the user wants to primarily rely on window walker to switch between all the windows on a desktop. This feature would save the time of having to backspace all the characters from last search history.

### Supporting information

_No response_

Start by reproducing the Window Walker behavior described: search for a window, switch to it, and reopen Window Walker. Confirm that the search field is empty after a successful switch, then verify that typing a new window name works immediately without backspacing.

Written by the indexing model from the issue text.