The search UI ships light and dark palettes. The Mode control sits at the top of the Color Theme in Elevated › Site Search › Settings › Theme & Style: pick Dark, save, and the box, results, and modal switch to the dark palette.
Navigate to Elevated › Site Search › Settings, open Theme & Style, and click Dark under Mode. The preview flips immediately.

Click Save Settings and reload a page with the search box:

The frontend stayed light after switching. Save from the settings page and reload the frontend; the mode travels together with the background color, so use the Mode buttons rather than editing single color values elsewhere.
Some elements stayed light in dark mode. They carry explicit overrides. Clear those fields under Override theme colors to let them derive from the dark palette.