For some reason gray area below search appears only in Private Mode, but if I disable every checkbox in Search settings, then there is no this area neither in Normal Mode, nor in Private mode. I guess, either you need to remove it from Private Mode to be consistent everywhere in the app or make it appears like Safari does.
Orion, OS version; hardware type:
Orion RC 0.99.124.4.3-rc (WebKit 6184.108.40.206.1)
macOS Version 13.4.1 (Build 22F82)
Orion Normal Mode (everything in search is disabled):
Orion Private Mode (everything in search is enabled):
Orion Private Mode (everything in search is disabled):
Safari (same in Private Mode):