At present the search bar does not expand when a longer query is entered. This poses issues when editing or revising queries, and for visual accessibility. Google implements this functionality well — see the behaviour difference in the screen recordings below.
Desktop, macOS, Safari (Kagi and Google)
Mobile, iOS, Safari (Kagi)
Mobile, iOS, Safari (Google)
The problem with implementing an expanded search bar is that it would clash with Kagi's existing drop-down functionality which displays suggested/related searches.
Kagi

Google

I think the best way around that is to simply expand the drop-down functionality and shift suggested results down, vertically expanding the search box to display the full query.