The inline search bar was permanently visible. Replace it with a search
action button (a 6-sided cookie shape, sibling to the settings cookie) to
the left of settings: the search bar is absent until tapped, then opens
expanded and auto-focused, covering the home content with live results.
Back arrow or system back closes it; the FAB hides only while searching.
Pass windowInsets = 0 so the bar, already below the app bar, does not
re-apply the status-bar inset and float with a large top gap.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>