[applet] Make search field always visible

Right now the search field is only visible when specifically activated by clicking on the search button. This was done because there used to be a ton of buttons on the toolbar row that made the search field's size and position look odd when sharing the same row. However with other recent changes, we no longer have this constraint and there is now plenty of room for the search field even including some generous padding to separate it from other controls. So let's put it there.

When hotspot is supported:

When hotspot is not supported:

cc @teams/vdg